Discussione:
I quattro "4"
(troppo vecchio per rispondere)
Chenickname
2019-08-09 15:20:16 UTC
Permalink
0 = 4-4+4-4
1 = 4/4x4/4
2 = 4/4+4/4
3 = 4-4^(4-4)
4 = 4+(4-4)x4
5 = 4+4^(4-4)
6 = 4+(4+4)/4
7 = 4+4-4/4
8 = 4+4+4-4
9 = 4+4+4/4
10 = (44-4)/4
11 = 44/sqr(4)/sqr(4)
12 = 4x(4-4/4)
13 = 44/4+sqr(4)
14 = 4+4+4+sqr(4)
15 = 44/4+4
16 = 4x4+4-4
17 = 4x4+4/4
18 = 4x4+4-sqr(4)
19 = 4!-4-4/4
20 = 4x4+sqr(4)+sqr(4)
21 = 4!-4+4/4
22 = 4!-sqr(4)+4-4
23 = 4!-4^(4-4)
24 = 4x4+4+4
25 = 4!+4^(4-4)
26 = 4!+sqr(4)+4-4
27 = 4!+4/4+sqr(4)
28 = 4!+4+4-4
29 = 4!+4+(4/4)=29
30 = 4!+(4-(4/4))!
31 = sqr(4)^int(ln(4)+4)-int(ln(4))=31
32 = 4x4x4/sqr(4)
33 = (4^int(ln(4!))+sqr(4))/sqr(4)
34 = 4!+4+4+sqr(4)
35 = 4x4x sqr(4)+int(ln(4!))
36 = 44-4-4
37 = 44-4-int(ln(4!))
38 = 44-4-sqr(4)
39 = 44-4-int(ln(4))
40 = 44-sqr(4)-sqr(4)
41 = 44-sqr(4)-int(ln(4))
42 = 44-4/sqr(4)
43 = 44-4+int(ln(4!))
44 = 44+4-4
45 = 44+4/4
46 = 44+4-sqr(4)
47 = 44+4-int(ln(4))
48 = 44+sqr(4)+sqr(4)
49 = 44+4+int(ln(4))
50 = 44+4+sqr(4)
51 = 44+4+int(ln(4!))
52 = 44+4+4
53 = 44+(int(ln(4!)))^sqr(4)
54 = (4+sqr(4)) x (int(ln(4!)))^sqr(4)
55 = 4^int(ln(4!)) - (int(ln(4!)))^sqr(4)
56 = 4^int(ln(4!))-4-4
57 = 4^int(ln(4!))-4-int(ln(4!))
58 = 4^int(ln(4!))-4-(4)
59 = 4^int(ln(4!))-4-int(ln(4))
60 = 4x4x4-4
61 = 4x4x4-int(ln(4!))
62 = 4x4x4-sqr(4)
63 = 4x4x4-int(ln(4))
64 = 4^int(ln(4!))+4-4
65 = 4^int(ln(4!))+4/4
66 = 4x4x4+sqr(4)
67 = 4x4x4+int(ln(4!))
68 = 4x4x4+4
69 = 4^int(ln(4!))+4+int(ln(4))
70 = 4^int(ln(4!))+4+sqr(4)
71 = 4^int(ln(4!))+4+int(ln(4!))
72 = 4^int(ln(4!))+4+4
73 = 4^int(ln(4!))+(int(ln(4!)))^sqr(4)
74 = 4^int(ln(4!))+4+(int(ln(4!)))!
75 = (int(ln(4!)))!x4x int(ln(4!)) +int(ln(4!))
76 = 4^int(ln(4!)) + (int(ln(4!)))! x sqr(4)
77 = 4! x int(ln(4!)) +4+int(ln(4))
78 = 4! x int(ln(4!)) +4+sqr(4)
79 = 4! x int(ln(4!)) +4+int(ln(4!))
80 = 4! x int(ln(4!)) +4+4
81 = 4! x int(ln(4!)) +(int(ln(4!)))^sqr(4)
82 = 44 x sqr(4) - (int(ln(4!)))!
83 = (int(ln(4!)))^(sqr(4) x sqr(4)) + sqr(4)
84 = (int(ln(4!)))! x (4+int(ln(4!))) x sqr(4)
85 = (int(ln(4!)))^(sqr(4) x sqr(4)) + 4
86 = (int(ln(4!)))^4+4+int(ln(4))
87 = (int(ln(4!)))^4+4+sqr(4)
88 = 44x4/sqr(4)
89 = 44xsqr(4)+int(ln(4))
90 = 44xsqr(4)+sqr(4)
91 = 44xsqr(4)+int(ln(41))
92 = 44xsqr(4)+4
93 = 4x4!-sqr(4)-int(ln(4))
94 = 4x4!-4+sqr(4)
95 = 4x4!-4+int(ln(4!))
96 = 4x4!+4-4
97 = 4x4!+sqr(4)-int(ln(4))
98 = 4x4!+4/sqr(4)
99 = 4x4!+4-int(ln(4))
100 = 4x4!+sqr(4)+sqr(4)

Quale sara' il primo intero non rappresentabile da quattro 4?

LZ

(io non lo so)
Yoda
2019-08-09 18:30:31 UTC
Permalink
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
Post by Chenickname
LZ
(io non lo so)
Ciao!
--
Yoda
Chenickname
2019-08-09 18:46:02 UTC
Permalink
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
Post by Chenickname
LZ
(io non lo so)
Ciao!
--
Yoda
444+int(ln(4))

:-)
Ciao!
Yoda
2019-08-09 19:41:48 UTC
Permalink
Post by Chenickname
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
444+int(ln(4))
:-)
Ho smirato di poco :-( ma vediamo adesso come lo fai il 3: 447 ciao

Apropos. Ma il .4 americano vale? perche' int(ln .4)=0, altrimenti anche
444 mi sa che non lo becchi ariciao
--
Yoda
Chenickname
2019-08-09 20:00:40 UTC
Permalink
Post by Yoda
Post by Chenickname
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
444+int(ln(4))
:-)
Ho smirato di poco :-( ma vediamo adesso come lo fai il 3: 447 ciao
Apropos. Ma il .4 americano vale? perche' int(ln .4)=0, altrimenti anche
444 mi sa che non lo becchi ariciao
--
Yoda
444 = 444 x int(ln(4))
447 = 444 + int(ln(4!))

:-)
Yoda
2019-08-09 20:41:34 UTC
Permalink
Post by Chenickname
Post by Yoda
Post by Chenickname
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
444+int(ln(4))
:-)
Ho smirato di poco :-( ma vediamo adesso come lo fai il 3: 447 ciao
Apropos. Ma il .4 americano vale? perche' int(ln .4)=0, altrimenti anche
444 mi sa che non lo becchi ariciao
444 = 444 x int(ln(4))
447 = 444 + int(ln(4!))
:-)
Ok con tre cifre sei un drago, provo quest'ultimo tentativo 4440, anzi
4447 che e' primo, ma mi sa che verro' battuto da un numero minore ciao
--
Yoda
Chenickname
2019-08-09 20:56:59 UTC
Permalink
Post by Yoda
Post by Chenickname
Post by Yoda
Post by Chenickname
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
444+int(ln(4))
:-)
Ho smirato di poco :-( ma vediamo adesso come lo fai il 3: 447 ciao
Apropos. Ma il .4 americano vale? perche' int(ln .4)=0, altrimenti anche
444 mi sa che non lo becchi ariciao
444 = 444 x int(ln(4))
447 = 444 + int(ln(4!))
:-)
Ok con tre cifre sei un drago, provo quest'ultimo tentativo 4440, anzi
4447 che e' primo, ma mi sa che verro' battuto da un numero minore ciao
--
Yoda
Per 4447 ho bisogno di sei "4":
4447 = ((int(ln(4!)))!)! x (int(ln(4!)))! + 4^4/sqr(4) - int(ln(4))
Ma penso che il primo intero non fattibile con quattro "4" sia molto piu' piccolo.

Ciao!
Chenickname
2019-08-09 20:57:57 UTC
Permalink
Post by Chenickname
Post by Yoda
Post by Chenickname
Post by Yoda
Post by Chenickname
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
445?
444+int(ln(4))
:-)
Ho smirato di poco :-( ma vediamo adesso come lo fai il 3: 447 ciao
Apropos. Ma il .4 americano vale? perche' int(ln .4)=0, altrimenti anche
444 mi sa che non lo becchi ariciao
444 = 444 x int(ln(4))
447 = 444 + int(ln(4!))
:-)
Ok con tre cifre sei un drago, provo quest'ultimo tentativo 4440, anzi
4447 che e' primo, ma mi sa che verro' battuto da un numero minore ciao
--
Yoda
4447 = ((int(ln(4!)))!)! x (int(ln(4!)))! + 4^4/sqr(4) - int(ln(4))
Ma penso che il primo intero non fattibile con quattro "4" sia molto piu' piccolo.
Ciao!
Non e' vero, bastavano cinque :-)
Yoda
2019-08-09 23:20:18 UTC
Permalink
Post by Chenickname
Non e' vero, bastavano cinque :-)
Occhio anche al semifattoriale (non dico per questo caso) che ad esempio
in un colpo solo ti da' 8 = 4!! ciao
--
Yoda
Chenickname
2019-08-10 09:18:20 UTC
Permalink
Post by Yoda
Post by Chenickname
Non e' vero, bastavano cinque :-)
Occhio anche al semifattoriale (non dico per questo caso) che ad esempio
in un colpo solo ti da' 8 = 4!! ciao
--
Yoda
Ottimo suggerimento, infatti mi ero impantanato su 197:

196 = (4!+4!)x4 + 4
197 = (4!!)!!/sqr(4)+4+int(ln(4))
198 = (4^int(ln(4!))+sqr(4)) x int(ln(4!))
199 = (4!!)!!/sqr(4)+4+int(ln(4!))
200 = (4!+4!+sqr(4)) x 4
201 = (4!!)!!/sqr(4) + (int(ln(4!)))^sqr(4)
Chenickname
2019-08-10 15:02:40 UTC
Permalink
Post by Chenickname
...
Quale sara' il primo intero non rappresentabile da quattro 4?
...
0 = 4-4+4-4
1 = 4/4x4/4
2 = 4/4+4/4
3 = 4-4^(4-4)
4 = 4+(4-4)x4
5 = 4+4^(4-4)
6 = 4+(4+4)/4
7 = 4+4-4/4
8 = 4+4+4-4
9 = 4+4+4/4
10 = (44-4)/4
11 = 44/sqr(4)/sqr(4)
12 = 4x(4-4/4)
13 = 44/4+sqr(4)
14 = 4+4+4+sqr(4)
15 = 44/4+4
16 = 4x4+4-4
17 = 4x4+4/4
18 = 4x4+4-sqr(4)
19 = 4!-4-4/4
20 = 4x4+sqr(4)+sqr(4)
21 = 4!-4+4/4
22 = 4!-sqr(4)+4-4
23 = 4!-4^(4-4)
24 = 4x4+4+4
25 = 4!+4^(4-4)
26 = 4!+sqr(4)+4-4
27 = 4!+4/4+sqr(4)
28 = 4!+4+4-4
29 = 4!+4+(4/4)=29
30 = 4!+(4-(4/4))!
31 = sqr(4)^int(ln(4)+4)-int(ln(4))=31
32 = 4x4x4/sqr(4)
33 = (4^int(ln(4!))+sqr(4))/sqr(4)
34 = 4!+4+4+sqr(4)
35 = 4x4x sqr(4)+int(ln(4!))
36 = 44-4-4
37 = 44-4-int(ln(4!))
38 = 44-4-sqr(4)
39 = 44-4-int(ln(4))
40 = 44-sqr(4)-sqr(4)
41 = 44-sqr(4)-int(ln(4))
42 = 44-4/sqr(4)
43 = 44-4+int(ln(4!))
44 = 44+4-4
45 = 44+4/4
46 = 44+4-sqr(4)
47 = 44+4-int(ln(4))
48 = 44+sqr(4)+sqr(4)
49 = 44+4+int(ln(4))
50 = 44+4+sqr(4)
51 = 44+4+int(ln(4!))
52 = 44+4+4
53 = 44+(int(ln(4!)))^sqr(4)
54 = (4+sqr(4)) x (int(ln(4!)))^sqr(4)
55 = 4^int(ln(4!)) - (int(ln(4!)))^sqr(4)
56 = 4^int(ln(4!))-4-4
57 = 4^int(ln(4!))-4-int(ln(4!))
58 = 4^int(ln(4!))-4-(4)
59 = 4^int(ln(4!))-4-int(ln(4))
60 = 4x4x4-4
61 = 4x4x4-int(ln(4!))
62 = 4x4x4-sqr(4)
63 = 4x4x4-int(ln(4))
64 = 4^int(ln(4!))+4-4
65 = 4^int(ln(4!))+4/4
66 = 4x4x4+sqr(4)
67 = 4x4x4+int(ln(4!))
68 = 4x4x4+4
69 = 4^int(ln(4!))+4+int(ln(4))
70 = 4^int(ln(4!))+4+sqr(4)
71 = 4^int(ln(4!))+4+int(ln(4!))
72 = 4^int(ln(4!))+4+4
73 = 4^int(ln(4!))+(int(ln(4!)))^sqr(4)
74 = 4^int(ln(4!))+4+(int(ln(4!)))!
75 = (int(ln(4!)))!x4x int(ln(4!)) +int(ln(4!))
76 = 4^int(ln(4!)) + (int(ln(4!)))! x sqr(4)
77 = 4! x int(ln(4!)) +4+int(ln(4))
78 = 4! x int(ln(4!)) +4+sqr(4)
79 = 4! x int(ln(4!)) +4+int(ln(4!))
80 = 4! x int(ln(4!)) +4+4
81 = 4! x int(ln(4!)) +(int(ln(4!)))^sqr(4)
82 = 44 x sqr(4) - (int(ln(4!)))!
83 = (int(ln(4!)))^(sqr(4) x sqr(4)) + sqr(4)
84 = (int(ln(4!)))! x (4+int(ln(4!))) x sqr(4)
85 = (int(ln(4!)))^(sqr(4) x sqr(4)) + 4
86 = (int(ln(4!)))^4+4+int(ln(4))
87 = (int(ln(4!)))^4+4+sqr(4)
88 = 44x4/sqr(4)
89 = 44xsqr(4)+int(ln(4))
90 = 44xsqr(4)+sqr(4)
91 = 44xsqr(4)+int(ln(41))
92 = 44xsqr(4)+4
93 = 4x4!-sqr(4)-int(ln(4))
94 = 4x4!-4+sqr(4)
95 = 4x4!-4+int(ln(4!))
96 = 4x4!+4-4
97 = 4x4!+sqr(4)-int(ln(4))
98 = 4x4!+4/sqr(4)
99 = 4x4!+4-int(ln(4))
100 = 4x4!+sqr(4)+sqr(4)
101 = 4x4!+4+int(ln(4))
102 = 4x4!+4+sqr(4)
103 = 4x4!+4+int(ln(4!))
104 = 4x4!+4+4
105 = 4x4!+(int(ln(4!)))^sqr(4)
106 = (int(ln(4!)))^(int(ln(4!)))x4-sqr(4)
107 = (int(ln(4!)))^(int(ln(4!)))x4-int(ln(4))
108 = (4!+4)x4-4
109 = (4!+4)x4-int(ln(4!))
110 = (4!+4)x4-sqr(4)
111 = (4!+4)x4-int(ln(4))
112 = (4!+4)x4 x int(ln(4))
113 = (4!+4)x4+int(ln(4))
114 = (4!+4)x4+sqr(4)
115 = (4!+4)x4+int(ln(4!))
116 = (4!+4)x4+4
117 = (4!+(int(ln(4!)))!)x4-int(ln(4!))
118 = (4!+(int(ln(4!)))!)x4-sqr(4)
119 = (4!+(int(ln(4!)))!)x4-int(ln(4))
120 = (4!+(int(ln(4!)))!)x4 x int(ln(4))
121 = (4!+(int(ln(4!)))!)x4+int(ln(4))
122 = (4!+(int(ln(4!)))!)x4+sqr(4)
123 = (4!+(int(ln(4!)))!)x4+int(ln(4!))
124 = 4^4/sqr(4)-4
125 = 4^4/sqr(4)-int(ln(4!))
126 = 4^4/sqr(4)-sqr(4)
127 = 4^4/sqr(4)-int(ln(4))
128 = 4^4/sqr(4) x int(ln(4))
129 = 4^4/sqr(4)+int(ln(4)
130 = 4^4/sqr(4)+sqr(4)
131 = 4^4/sqr(4)+int(ln(4!))
132 = 4^4/sqr(4)+4
133 = 44 x Int(ln(4!)) + int(ln(4))
134 = 44 x Int(ln(4!)) + sqr(4)
135 = 44 x Int(ln(4!)) + int(ln(4!))
136 = 44 x Int(ln(4!)) + 4
137 = 4!x(int(ln(4!)))! -4-int(ln(4!))
138 = 4!x(int(ln(4!)))! -4-sqr(4)
139 = 4!x(int(ln(4!)))! -4-int(ln(4))
140 = 4!x(int(ln(4!)))! -sqr(4)-sqr(4)
141 = 4!x(int(ln(4!)))! - int(ln(4!)) x int(ln(4))
142 = 4!x(int(ln(4!)))! - sqr(4) x int(ln(4))
143 = 4!x(int(ln(4!)))! - int(ln(4)) x int(ln(4))
144 = 4!x(int(ln(4!)))! +4-4
145 = 4!x(int(ln(4!)))! +4-int(ln(4!))
146 = 4!x(int(ln(4!)))! +4-sqr(4)
147 = 4!x(int(ln(4!)))! +4-int(ln(4))
148 = 4!x(int(ln(4!)))! +4 x int(ln(4))
149 = 4!x(int(ln(4!)))! +4 + int(ln(4))
150 = 4!x(int(ln(4!)))! +4+sqr(4)
151 = 4!x(int(ln(4!)))! +4+int(ln(4!))
152 = 4!x(int(ln(4!)))! +4+4
153 = (4!+sqr(4)) x (int(ln(4!)))! - int(ln(4!))
154 = (4!+sqr(4)) x (int(ln(4!)))! - sqr(4)
155 = (4!+sqr(4)) x (int(ln(4!)))! - int(ln(4))
156 = (4!+sqr(4)) x (int(ln(4!)))! x int(ln(4))
157 = (4!+sqr(4)) x (int(ln(4!)))! + int(ln(4))
158 = (4!+sqr(4)) x (int(ln(4!)))! + sqr(4)
159 = (4!+sqr(4)) x (int(ln(4!)))! + int(ln(4!))
160 = (44-4)x4
161 = (4!+int(ln(4!))) x (int(ln(4!)))! - int(ln(4))
162 = (4!+int(ln(4!))) x (int(ln(4!)))! x int(ln(4))
163 = (4!+int(ln(4!))) x (int(ln(4!)))! + int(ln(4))
164 = (4!+int(ln(4!))) x (int(ln(4!)))! + sqr(4)
165 = (4!+int(ln(4!))) x (int(ln(4!)))! + int(ln(4!))
166 = (4!+int(ln(4!))) x (int(ln(4!)))! + 4
167 = (4!+4) x (int(ln(4!)))! - int(ln(4))
168 = (4!+4) x (int(ln(4!)))! x int(ln(4))
169 = (4!+4) x (int(ln(4!)))! + int(ln(4))
170 = (4!+4) x (int(ln(4!)))! + sqr(4)
171 = (4!+4) x (int(ln(4!)))! + int(ln(4!))
172 = 44x4 - 4
173 = 44x4 - int(ln(4!))
174 = 44x4 - sqr(4)
175 = 44x4 - int(ln(4))
176 = 44x4 x int(ln(4))
177 = 44x4 + int(ln(4))
178 = 44x4 + sqr(4)
179 = 44x4 + int(ln(4!))
180 = 44x4 + 4
181 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + int(ln(4))
182 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + sqr(4)
183 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + int(ln(4!))
184 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + 4
185 = ((int(ln(4!)))!)!/4 +4+int(ln(4))
186 = ((int(ln(4!)))!)!/4 +4+sqr(4)
187 = ((int(ln(4!)))!)!/4 +4+int(ln(4!))
188 = ((int(ln(4!)))!)!/4 +4+4
189 = ((int(ln(4!)))!)!/4 +(int(ln(4!)))^sqr(4)
190 = (4!+4!)x4 - sqr(4)
191 = (4!+4!)x4 - int(ln(4))
192 = (44+4)x4
193 = (4!+4!)x4 + int(ln(4))
194 = (4!+4!)x4 + sqr(4)
195 = (4!+4!)x4 + int(ln(4!))
196 = (4!+4!)x4 + 4
197 = (4!!)!!/sqr(4)+4+int(ln(4))
198 = (4^int(ln(4!))+sqr(4)) x int(ln(4!))
199 = (4!!)!!/sqr(4)+4+int(ln(4!))
200 = (4!+4!+sqr(4)) x 4
201 = (4!!)!!/sqr(4) + (int(ln(4!)))^sqr(4)
202 = ((4!!)!!+4!)/sqr(4)-sqr(4)
203 = ((4!!)!!+4!)/sqr(4)-int(ln(4))
204 = ((4!!)!!+4!)/sqr(4) x int(ln(4))
205 = ((4!!)!!+4!)/sqr(4)+int(ln(4))
206 = ((4!!)!!+4!)/sqr(4)+sqr(4)
207 = ((4!!)!!+4!)/sqr(4)+int(ln(4!))
208 = ((4!!)!!+4!)/sqr(4)+4
209 = (((int(ln(4!)))!)!!+4)x4 + int(ln(4))
210 = (((int(ln(4!)))!)!!+4)x4 + sqr(4)
211 = (((int(ln(4!)))!)!!+4)x4 + int(ln(4!))
212 = (((int(ln(4!)))!)!!+4)x4 + 4
213 = (4+int(ln(4!)))!! x sqr(4) + int(ln(4!))
214 = (4+int(ln(4!)))!! x sqr(4) + 4
215 = ((4!!)!!+(int(ln(4!)))!)x4 - int(ln(4))
216 = ((4!!)!!+(int(ln(4!)))!)x4 x int(ln(4))
217 = ((4!!)!!+(int(ln(4!)))!)x4 + int(ln(4))
218 = ((4!!)!!+(int(ln(4!)))!)x4 + sqr(4)
219 = ((4!!)!!+(int(ln(4!)))!)x4 + int(ln(4!))
220 = (((int(ln(4!)))!)!!+4!!)x4 - 4
221 = (((int(ln(4!)))!)!!+4!!)x4 - int(ln(4!))
222 = (((int(ln(4!)))!)!!+4!!)x4 - sqr(4)
223 = (((int(ln(4!)))!)!!+4!!)x4 - int(ln(4))
224 = (((int(ln(4!)))!)!!+4!!)x4 x int(ln(4))
225 = (((int(ln(4!)))!)!!+4!!)x4 + int(ln(4))
226 = (((int(ln(4!)))!)!!+4!!)x4 + sqr(4)
227 = (((int(ln(4!)))!)!!+4!!)x4 + int(ln(4!))
228 = (((int(ln(4!)))!)!!+4!!)x4 + 4
229 = ((4+int(ln(4)))!!)^sqr(4)+4
230 = (4!+4)x4!! + (int(ln(4!)))!
231 = 4^4-4! - int(ln(4))
232 = 4^4-4! x int(ln(4))
233 = 4^4-4! + int(ln(4))
234 = 4^4-4! + sqr(4)
235 = 4^4-4! + int(ln(4!))
236 = 4^4-4! + 4
237 = int(((int(ln(4!)))^sqr(4))!!/4) + int(ln(4))
238 = int(((int(ln(4!)))^sqr(4))!!/4) + sqr(4)
239 = int(((int(ln(4!)))^sqr(4))!!/4) + int(ln(4!))
240 = 4^4-4x4
241 = (int(ln(4!))!)! / int(ln(4!)) +4-int(ln(4!))
242 = (int(ln(4!))!)! / int(ln(4!)) +4-sqr(4)
243 = (int(ln(4!))!)! / int(ln(4!)) +4-int(ln(4))
244 = (int(ln(4!))!)! / int(ln(4!)) +4 x int(ln(4))
245 = (int(ln(4!))!)! / int(ln(4!)) +4+int(ln(4))
246 = (int(ln(4!))!)! / int(ln(4!)) +4+sqr(4)
247 = (int(ln(4!))!)! / int(ln(4!)) +4+int(ln(4!))
248 = (int(ln(4!))!)! / int(ln(4!)) +4+4
249 = (int(ln(4!))!)! / int(ln(4!)) +(int(ln(4!)))^sqr(4)
250 = 4^4-(int(ln(4!)))! x int(ln(4))
251 = 4^4-(int(ln(4!)))! + int(ln(4))
252 = 4^4-(int(ln(4!)))! + sqr(4)
253 = 4^4-(int(ln(4!)))! + int(ln(4!))
254 = 4^4-(int(ln(4!)))! + 4
255 = 4^4-int(ln(4)) x int(ln(4))
256 = 4^4+4-4
257 = 4^4+4-int(ln(4!))
258 = 4^4+4-sqr(4)
259 = 4^4+4-int(ln(4))
260 = 4^4+sqr(4x4)
261 = 4^4+4+int(ln(4))
262 = 4^4+4+sqr(4)
263 = 4^4+4+int(ln(4!))
264 = 4^4+4+4
265 = 4^4+(int(ln(4!)))^sqr(4)
266 = 4^4+4+(int(ln(4!)))!
267 = 4^4+4!!+int(ln(4!))
268 = 4^4+4!!+4
269 = int((int(ln(4!)))^(4!!)/4!) - 4
270 = int((int(ln(4!)))^(4!!)/4!) - int(ln(4!))
271 = int((int(ln(4!)))^(4!!)/4!) - sqr(4)
272 = int((int(ln(4!)))^(4!!)/4!) - int(ln(4))
273 = int((int(ln(4!)))^(4!!)/4!) x int(ln(4))
274 = int((int(ln(4!)))^(4!!)/4!) + int(ln(4))
275 = int((int(ln(4!)))^(4!!)/4!) + sqr(4)
276 = int((int(ln(4!)))^(4!!)/4!) + int(ln(4!))
277 = int((int(ln(4!)))^(4!!)/4!) + 4
278 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -(int(ln(4!)))! -4
279 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -(int(ln(4!)))^sqr(4)
280 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4-4
281 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4!)) -4
282 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(4) -4
283 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4)) -4
284 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(4x4)
285 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4)) -sqr(4)
286 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(sqr(4x4))
287 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4/4
288 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4+4
289 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +4/4
290 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(sqr(4x4))
291 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4)) +sqr(4)
292 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(4x4)
293 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4)) +4
294 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(4) +4
295 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4!)) +4
296 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +4+4
297 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +(int(ln(4!)))^sqr(4)
298 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +(int(ln(4!)))! +4
299 = (((int(ln(4!)))^sqr(4))!! - ((int(ln(4!)))!)!!)/int(ln(4!))
300 = ((int(ln(4!)))!)!! x (int(ln(4!)))! + (int(ln(4!)))! x sqr(4)

Ci saranno sicuramente degli errori.

"Sono un po' stanchino"

LZ
Ciao
Giorgio Vecchi
2019-08-11 08:25:51 UTC
Permalink
Post by Chenickname
300 = ((int(ln(4!)))!)!! x (int(ln(4!)))! + (int(ln(4!)))! x sqr(4)
300 = 4^4 + 44

... ma solo perché mi ci è cascato l'occhio. Degli altri mi fido ciecamente!
;)

Ciao Livio! :)

Giorgio
Chenickname
2019-08-11 10:28:13 UTC
Permalink
Post by Giorgio Vecchi
Post by Chenickname
300 = ((int(ln(4!)))!)!! x (int(ln(4!)))! + (int(ln(4!)))! x sqr(4)
300 = 4^4 + 44
... ma solo perché mi ci è cascato l'occhio. Degli altri mi fido ciecamente!
;)
Ciao Livio! :)
Giorgio
Bello!
Ciao Giorgio!
Livio
Chenickname
2019-08-11 11:38:54 UTC
Permalink
Post by Chenickname
Post by Chenickname
...
Quale sara' il primo intero non rappresentabile da quattro 4?
...
0 = 4-4+4-4
1 = 4/4x4/4
2 = 4/4+4/4
3 = 4-4^(4-4)
4 = 4+(4-4)x4
5 = 4+4^(4-4)
6 = 4+(4+4)/4
7 = 4+4-4/4
8 = 4+4+4-4
9 = 4+4+4/4
10 = (44-4)/4
11 = 44/sqr(4)/sqr(4)
12 = 4x(4-4/4)
13 = 44/4+sqr(4)
14 = 4+4+4+sqr(4)
15 = 44/4+4
16 = 4x4+4-4
17 = 4x4+4/4
18 = 4x4+4-sqr(4)
19 = 4!-4-4/4
20 = 4x4+sqr(4)+sqr(4)
21 = 4!-4+4/4
22 = 4!-sqr(4)+4-4
23 = 4!-4^(4-4)
24 = 4x4+4+4
25 = 4!+4^(4-4)
26 = 4!+sqr(4)+4-4
27 = 4!+4/4+sqr(4)
28 = 4!+4+4-4
29 = 4!+4+(4/4)=29
30 = 4!+(4-(4/4))!
31 = sqr(4)^int(ln(4)+4)-int(ln(4))=31
32 = 4x4x4/sqr(4)
33 = (4^int(ln(4!))+sqr(4))/sqr(4)
34 = 4!+4+4+sqr(4)
35 = 4x4x sqr(4)+int(ln(4!))
36 = 44-4-4
37 = 44-4-int(ln(4!))
38 = 44-4-sqr(4)
39 = 44-4-int(ln(4))
40 = 44-sqr(4)-sqr(4)
41 = 44-sqr(4)-int(ln(4))
42 = 44-4/sqr(4)
43 = 44-4+int(ln(4!))
44 = 44+4-4
45 = 44+4/4
46 = 44+4-sqr(4)
47 = 44+4-int(ln(4))
48 = 44+sqr(4)+sqr(4)
49 = 44+4+int(ln(4))
50 = 44+4+sqr(4)
51 = 44+4+int(ln(4!))
52 = 44+4+4
53 = 44+(int(ln(4!)))^sqr(4)
54 = (4+sqr(4)) x (int(ln(4!)))^sqr(4)
55 = 4^int(ln(4!)) - (int(ln(4!)))^sqr(4)
56 = 4^int(ln(4!))-4-4
57 = 4^int(ln(4!))-4-int(ln(4!))
58 = 4^int(ln(4!))-4-(4)
59 = 4^int(ln(4!))-4-int(ln(4))
60 = 4x4x4-4
61 = 4x4x4-int(ln(4!))
62 = 4x4x4-sqr(4)
63 = 4x4x4-int(ln(4))
64 = 4^int(ln(4!))+4-4
65 = 4^int(ln(4!))+4/4
66 = 4x4x4+sqr(4)
67 = 4x4x4+int(ln(4!))
68 = 4x4x4+4
69 = 4^int(ln(4!))+4+int(ln(4))
70 = 4^int(ln(4!))+4+sqr(4)
71 = 4^int(ln(4!))+4+int(ln(4!))
72 = 4^int(ln(4!))+4+4
73 = 4^int(ln(4!))+(int(ln(4!)))^sqr(4)
74 = 4^int(ln(4!))+4+(int(ln(4!)))!
75 = (int(ln(4!)))!x4x int(ln(4!)) +int(ln(4!))
76 = 4^int(ln(4!)) + (int(ln(4!)))! x sqr(4)
77 = 4! x int(ln(4!)) +4+int(ln(4))
78 = 4! x int(ln(4!)) +4+sqr(4)
79 = 4! x int(ln(4!)) +4+int(ln(4!))
80 = 4! x int(ln(4!)) +4+4
81 = 4! x int(ln(4!)) +(int(ln(4!)))^sqr(4)
82 = 44 x sqr(4) - (int(ln(4!)))!
83 = (int(ln(4!)))^(sqr(4) x sqr(4)) + sqr(4)
84 = (int(ln(4!)))! x (4+int(ln(4!))) x sqr(4)
85 = (int(ln(4!)))^(sqr(4) x sqr(4)) + 4
86 = (int(ln(4!)))^4+4+int(ln(4))
87 = (int(ln(4!)))^4+4+sqr(4)
88 = 44x4/sqr(4)
89 = 44xsqr(4)+int(ln(4))
90 = 44xsqr(4)+sqr(4)
91 = 44xsqr(4)+int(ln(41))
92 = 44xsqr(4)+4
93 = 4x4!-sqr(4)-int(ln(4))
94 = 4x4!-4+sqr(4)
95 = 4x4!-4+int(ln(4!))
96 = 4x4!+4-4
97 = 4x4!+sqr(4)-int(ln(4))
98 = 4x4!+4/sqr(4)
99 = 4x4!+4-int(ln(4))
100 = 4x4!+sqr(4)+sqr(4)
101 = 4x4!+4+int(ln(4))
102 = 4x4!+4+sqr(4)
103 = 4x4!+4+int(ln(4!))
104 = 4x4!+4+4
105 = 4x4!+(int(ln(4!)))^sqr(4)
106 = (int(ln(4!)))^(int(ln(4!)))x4-sqr(4)
107 = (int(ln(4!)))^(int(ln(4!)))x4-int(ln(4))
108 = (4!+4)x4-4
109 = (4!+4)x4-int(ln(4!))
110 = (4!+4)x4-sqr(4)
111 = (4!+4)x4-int(ln(4))
112 = (4!+4)x4 x int(ln(4))
113 = (4!+4)x4+int(ln(4))
114 = (4!+4)x4+sqr(4)
115 = (4!+4)x4+int(ln(4!))
116 = (4!+4)x4+4
117 = (4!+(int(ln(4!)))!)x4-int(ln(4!))
118 = (4!+(int(ln(4!)))!)x4-sqr(4)
119 = (4!+(int(ln(4!)))!)x4-int(ln(4))
120 = (4!+(int(ln(4!)))!)x4 x int(ln(4))
121 = (4!+(int(ln(4!)))!)x4+int(ln(4))
122 = (4!+(int(ln(4!)))!)x4+sqr(4)
123 = (4!+(int(ln(4!)))!)x4+int(ln(4!))
124 = 4^4/sqr(4)-4
125 = 4^4/sqr(4)-int(ln(4!))
126 = 4^4/sqr(4)-sqr(4)
127 = 4^4/sqr(4)-int(ln(4))
128 = 4^4/sqr(4) x int(ln(4))
129 = 4^4/sqr(4)+int(ln(4)
130 = 4^4/sqr(4)+sqr(4)
131 = 4^4/sqr(4)+int(ln(4!))
132 = 4^4/sqr(4)+4
133 = 44 x Int(ln(4!)) + int(ln(4))
134 = 44 x Int(ln(4!)) + sqr(4)
135 = 44 x Int(ln(4!)) + int(ln(4!))
136 = 44 x Int(ln(4!)) + 4
137 = 4!x(int(ln(4!)))! -4-int(ln(4!))
138 = 4!x(int(ln(4!)))! -4-sqr(4)
139 = 4!x(int(ln(4!)))! -4-int(ln(4))
140 = 4!x(int(ln(4!)))! -sqr(4)-sqr(4)
141 = 4!x(int(ln(4!)))! - int(ln(4!)) x int(ln(4))
142 = 4!x(int(ln(4!)))! - sqr(4) x int(ln(4))
143 = 4!x(int(ln(4!)))! - int(ln(4)) x int(ln(4))
144 = 4!x(int(ln(4!)))! +4-4
145 = 4!x(int(ln(4!)))! +4-int(ln(4!))
146 = 4!x(int(ln(4!)))! +4-sqr(4)
147 = 4!x(int(ln(4!)))! +4-int(ln(4))
148 = 4!x(int(ln(4!)))! +4 x int(ln(4))
149 = 4!x(int(ln(4!)))! +4 + int(ln(4))
150 = 4!x(int(ln(4!)))! +4+sqr(4)
151 = 4!x(int(ln(4!)))! +4+int(ln(4!))
152 = 4!x(int(ln(4!)))! +4+4
153 = (4!+sqr(4)) x (int(ln(4!)))! - int(ln(4!))
154 = (4!+sqr(4)) x (int(ln(4!)))! - sqr(4)
155 = (4!+sqr(4)) x (int(ln(4!)))! - int(ln(4))
156 = (4!+sqr(4)) x (int(ln(4!)))! x int(ln(4))
157 = (4!+sqr(4)) x (int(ln(4!)))! + int(ln(4))
158 = (4!+sqr(4)) x (int(ln(4!)))! + sqr(4)
159 = (4!+sqr(4)) x (int(ln(4!)))! + int(ln(4!))
160 = (44-4)x4
161 = (4!+int(ln(4!))) x (int(ln(4!)))! - int(ln(4))
162 = (4!+int(ln(4!))) x (int(ln(4!)))! x int(ln(4))
163 = (4!+int(ln(4!))) x (int(ln(4!)))! + int(ln(4))
164 = (4!+int(ln(4!))) x (int(ln(4!)))! + sqr(4)
165 = (4!+int(ln(4!))) x (int(ln(4!)))! + int(ln(4!))
166 = (4!+int(ln(4!))) x (int(ln(4!)))! + 4
167 = (4!+4) x (int(ln(4!)))! - int(ln(4))
168 = (4!+4) x (int(ln(4!)))! x int(ln(4))
169 = (4!+4) x (int(ln(4!)))! + int(ln(4))
170 = (4!+4) x (int(ln(4!)))! + sqr(4)
171 = (4!+4) x (int(ln(4!)))! + int(ln(4!))
172 = 44x4 - 4
173 = 44x4 - int(ln(4!))
174 = 44x4 - sqr(4)
175 = 44x4 - int(ln(4))
176 = 44x4 x int(ln(4))
177 = 44x4 + int(ln(4))
178 = 44x4 + sqr(4)
179 = 44x4 + int(ln(4!))
180 = 44x4 + 4
181 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + int(ln(4))
182 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + sqr(4)
183 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + int(ln(4!))
184 = (4!+(int(ln(4!)))!) x int(ln(4!)))! + 4
185 = ((int(ln(4!)))!)!/4 +4+int(ln(4))
186 = ((int(ln(4!)))!)!/4 +4+sqr(4)
187 = ((int(ln(4!)))!)!/4 +4+int(ln(4!))
188 = ((int(ln(4!)))!)!/4 +4+4
189 = ((int(ln(4!)))!)!/4 +(int(ln(4!)))^sqr(4)
190 = (4!+4!)x4 - sqr(4)
191 = (4!+4!)x4 - int(ln(4))
192 = (44+4)x4
193 = (4!+4!)x4 + int(ln(4))
194 = (4!+4!)x4 + sqr(4)
195 = (4!+4!)x4 + int(ln(4!))
196 = (4!+4!)x4 + 4
197 = (4!!)!!/sqr(4)+4+int(ln(4))
198 = (4^int(ln(4!))+sqr(4)) x int(ln(4!))
199 = (4!!)!!/sqr(4)+4+int(ln(4!))
200 = (4!+4!+sqr(4)) x 4
201 = (4!!)!!/sqr(4) + (int(ln(4!)))^sqr(4)
202 = ((4!!)!!+4!)/sqr(4)-sqr(4)
203 = ((4!!)!!+4!)/sqr(4)-int(ln(4))
204 = ((4!!)!!+4!)/sqr(4) x int(ln(4))
205 = ((4!!)!!+4!)/sqr(4)+int(ln(4))
206 = ((4!!)!!+4!)/sqr(4)+sqr(4)
207 = ((4!!)!!+4!)/sqr(4)+int(ln(4!))
208 = ((4!!)!!+4!)/sqr(4)+4
209 = (((int(ln(4!)))!)!!+4)x4 + int(ln(4))
210 = (((int(ln(4!)))!)!!+4)x4 + sqr(4)
211 = (((int(ln(4!)))!)!!+4)x4 + int(ln(4!))
212 = (((int(ln(4!)))!)!!+4)x4 + 4
213 = (4+int(ln(4!)))!! x sqr(4) + int(ln(4!))
214 = (4+int(ln(4!)))!! x sqr(4) + 4
215 = ((4!!)!!+(int(ln(4!)))!)x4 - int(ln(4))
216 = ((4!!)!!+(int(ln(4!)))!)x4 x int(ln(4))
217 = ((4!!)!!+(int(ln(4!)))!)x4 + int(ln(4))
218 = ((4!!)!!+(int(ln(4!)))!)x4 + sqr(4)
219 = ((4!!)!!+(int(ln(4!)))!)x4 + int(ln(4!))
220 = (((int(ln(4!)))!)!!+4!!)x4 - 4
221 = (((int(ln(4!)))!)!!+4!!)x4 - int(ln(4!))
222 = (((int(ln(4!)))!)!!+4!!)x4 - sqr(4)
223 = (((int(ln(4!)))!)!!+4!!)x4 - int(ln(4))
224 = (((int(ln(4!)))!)!!+4!!)x4 x int(ln(4))
225 = (((int(ln(4!)))!)!!+4!!)x4 + int(ln(4))
226 = (((int(ln(4!)))!)!!+4!!)x4 + sqr(4)
227 = (((int(ln(4!)))!)!!+4!!)x4 + int(ln(4!))
228 = (((int(ln(4!)))!)!!+4!!)x4 + 4
229 = ((4+int(ln(4)))!!)^sqr(4)+4
230 = (4!+4)x4!! + (int(ln(4!)))!
231 = 4^4-4! - int(ln(4))
232 = 4^4-4! x int(ln(4))
233 = 4^4-4! + int(ln(4))
234 = 4^4-4! + sqr(4)
235 = 4^4-4! + int(ln(4!))
236 = 4^4-4! + 4
237 = int(((int(ln(4!)))^sqr(4))!!/4) + int(ln(4))
238 = int(((int(ln(4!)))^sqr(4))!!/4) + sqr(4)
239 = int(((int(ln(4!)))^sqr(4))!!/4) + int(ln(4!))
240 = 4^4-4x4
241 = (int(ln(4!))!)! / int(ln(4!)) +4-int(ln(4!))
242 = (int(ln(4!))!)! / int(ln(4!)) +4-sqr(4)
243 = (int(ln(4!))!)! / int(ln(4!)) +4-int(ln(4))
244 = (int(ln(4!))!)! / int(ln(4!)) +4 x int(ln(4))
245 = (int(ln(4!))!)! / int(ln(4!)) +4+int(ln(4))
246 = (int(ln(4!))!)! / int(ln(4!)) +4+sqr(4)
247 = (int(ln(4!))!)! / int(ln(4!)) +4+int(ln(4!))
248 = (int(ln(4!))!)! / int(ln(4!)) +4+4
249 = (int(ln(4!))!)! / int(ln(4!)) +(int(ln(4!)))^sqr(4)
250 = 4^4-(int(ln(4!)))! x int(ln(4))
251 = 4^4-(int(ln(4!)))! + int(ln(4))
252 = 4^4-(int(ln(4!)))! + sqr(4)
253 = 4^4-(int(ln(4!)))! + int(ln(4!))
254 = 4^4-(int(ln(4!)))! + 4
255 = 4^4-int(ln(4)) x int(ln(4))
256 = 4^4+4-4
257 = 4^4+4-int(ln(4!))
258 = 4^4+4-sqr(4)
259 = 4^4+4-int(ln(4))
260 = 4^4+sqr(4x4)
261 = 4^4+4+int(ln(4))
262 = 4^4+4+sqr(4)
263 = 4^4+4+int(ln(4!))
264 = 4^4+4+4
265 = 4^4+(int(ln(4!)))^sqr(4)
266 = 4^4+4+(int(ln(4!)))!
267 = 4^4+4!!+int(ln(4!))
268 = 4^4+4!!+4
269 = int((int(ln(4!)))^(4!!)/4!) - 4
270 = int((int(ln(4!)))^(4!!)/4!) - int(ln(4!))
271 = int((int(ln(4!)))^(4!!)/4!) - sqr(4)
272 = int((int(ln(4!)))^(4!!)/4!) - int(ln(4))
273 = int((int(ln(4!)))^(4!!)/4!) x int(ln(4))
274 = int((int(ln(4!)))^(4!!)/4!) + int(ln(4))
275 = int((int(ln(4!)))^(4!!)/4!) + sqr(4)
276 = int((int(ln(4!)))^(4!!)/4!) + int(ln(4!))
277 = int((int(ln(4!)))^(4!!)/4!) + 4
278 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -(int(ln(4!)))! -4
279 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -(int(ln(4!)))^sqr(4)
280 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4-4
281 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4!)) -4
282 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(4) -4
283 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4)) -4
284 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(4x4)
285 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -int(ln(4)) -sqr(4)
286 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -sqr(sqr(4x4))
287 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4/4
288 = ((int(ln(4!)))!)!! x (int(ln(4!)))! -4+4
289 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +4/4
290 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(sqr(4x4))
291 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4)) +sqr(4)
292 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(4x4)
293 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4)) +4
294 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +sqr(4) +4
295 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +int(ln(4!)) +4
296 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +4+4
297 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +(int(ln(4!)))^sqr(4)
298 = ((int(ln(4!)))!)!! x (int(ln(4!)))! +(int(ln(4!)))! +4
299 = (((int(ln(4!)))^sqr(4))!! - ((int(ln(4!)))!)!!)/int(ln(4!))
300 = ((int(ln(4!)))!)!! x (int(ln(4!)))! + (int(ln(4!)))! x sqr(4)
Ci saranno sicuramente degli errori.
"Sono un po' stanchino"
LZ
Ciao
Intanto sarei arrivato qua, poi mi fermo per qualche giorno.

301 = ((int(ln(4!)))!)!! + sqr(4)) x (int(ln(4!)))! + int(ln(4))
302 = ((int(ln(4!)))!)!! + sqr(4)) x (int(ln(4!)))! + sqr(4)
303 = ((int(ln(4!)))!)!! + sqr(4)) x (int(ln(4!)))! + int(ln(4!))
304 = ((int(ln(4!)))!)!! + sqr(4)) x (int(ln(4!)))! + 4
305 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! - int(ln(4))
306 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! x int(ln(4))
307 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! + int(ln(4))
308 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! + sqr(4)
309 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! + int(ln(4!))
310 = ((int(ln(4!)))!)!! + int(ln(4!))) x (int(ln(4!)))! + 4
311 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! - int(ln(4))
312 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! x int(ln(4))
312 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! + int(ln(4))
312 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! + sqr(4)
312 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! + int(ln(4!))
312 = ((int(ln(4!)))!)!! + 4) x (int(ln(4!)))! + 4
313 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) - sqr(4)
314 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) - int(ln(4))
315 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) x int(ln(4))
316 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) + int(ln(4))
317 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) + sqr(4)
318 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) + int(ln(4!))
319 = ((int(ln(4!)))^sqr(4))!! / int(ln(4!)) + 4
320 = (4!!)!!-4^(int(ln(4!))) x int(ln(4))
321 = (4!!)!!-4^(int(ln(4!))) + int(ln(4))
322 = (4!!)!!-4^(int(ln(4!))) + sqr(4)
323 = (4!!)!!-4^(int(ln(4!))) + int(ln(4!))
324 = (4!!)!!-4^(int(ln(4!))) + 4
325 = (4!!)!! -((int(ln(4!)))!)!! - 4!! - int(ln(4!))
326 = (4!!)!! -((int(ln(4!)))!)!! - 4!! - sqr(4)
327 = (4!!)!! -((int(ln(4!)))!)!! - 4!! - int(ln(4))
328 = (4!!)!! -((int(ln(4!)))!)!! - 4!! x int(ln(4))
329 = (4!!)!! -((int(ln(4!)))!)!! - 4!! + int(ln(4))
330 = (4!!)!! -((int(ln(4!)))!)!! - 4!! + sqr(4)
331 = (4!!)!! -((int(ln(4!)))!)!! - 4!! + int(ln(4!))
332 = (4!!)!! -((int(ln(4!)))!)!! - sqr(4x4)
333 = (4!!)!! -((int(ln(4!)))!)!! - int(ln(4!)) x int(ln(4))
334 = (4!!)!! -((int(ln(4!)))!)!! - sqr(sqr(4x4))
335 = (4!!)!! -((int(ln(4!)))!)!! - int(ln(4)) x int(ln(4))
336 = (4!!)!! -((int(ln(4!)))!)!! - 4+4
337 = (4!!)!! -((int(ln(4!)))!)!! + 4 -int(ln(4!))
338 = (4!!)!! -((int(ln(4!)))!)!! + 4 -sqr(4)
339 = (4!!)!! -((int(ln(4!)))!)!! + 4 -int(ln(4))
340 = (4!!)!! -((int(ln(4!)))!)!! + 4 x int(ln(4))
341 = (4!!)!! -((int(ln(4!)))!)!! + 4 + int(ln(4))
342 = (4!!)!! -((int(ln(4!)))!)!! + 4 + sqr(4)
343 = (4!!)!! -((int(ln(4!)))!)!! + 4 + int(ln(4!))
344 = (4!!)!! -((int(ln(4!)))!)!! + 4 + 4
345 = (4!!)!! -((int(ln(4!)))!)!! + 4!! + int(ln(4))
346 = (4!!)!! -((int(ln(4!)))!)!! + 4!! + sqr(4)
347 = (4!!)!! -((int(ln(4!)))!)!! + 4!! + int(ln(4!))
348 = (4!!)!! -((int(ln(4!)))!)!! + 4!! + 4
349 = (4!!)!! - 4! - 4!! - int(ln(4!))
350 = (4!!)!! - 4! - 4!! - sqr(4)
351 = (4!!)!! - 4! - 4!! - int(ln(4))
352 = (4!!)!! - 4! - 4 - 4
353 = (4!!)!! - 4! - 4 - int(ln(4!))
354 = (4!!)!! - 4! - 4 - sqr(4)
355 = (4!!)!! - 4! - 4 - int(ln(4))
356 = (4!!)!! - 4! - 4 x int(ln(4))
357 = (4!!)!! - 4! - 4 + int(ln(4))
358 = (4!!)!! - 4! - 4 + sqr(4)
359 = (4!!)!! - 4! - 4 + int(ln(4!))
360 = (4!!)!! - 4! + 4 - 4
361 = (4!!)!! - 4! + 4 - int(ln(4!))
362 = (4!!)!! - 4! + 4 - sqr(4)
363 = (4!!)!! - 4! + 4 - int(ln(4))
364 = (4!!)!! - 4! + 4 x int(ln(4))
365 = (4!!)!! - 4! + 4 + int(ln(4))
366 = (4!!)!! - 4! + 4 + sqr(4)
367 = (4!!)!! - 4! + 4 + int(ln(4!))
368 = (4!!)!! - 4! + 4 + 4
369 = (4!!)!! - 4x4 + int(ln(4))
370 = (4!!)!! - 4x4 + sqr(4)
371 = (4!!)!! - 4x4 + int(ln(4!))
372 = (4!!)!! - 4x4 + 4
373 = (4!!)!! - 4!! - 4 + int(ln(4))
374 = (4!!)!! - 4!! - 4 + sqr(4)
375 = (4!!)!! - 4!! - 4 + int(ln(4!))
376 = (4!!)!! - 4!! + 4 - 4
377 = (4!!)!! - 4!! + 4 - int(ln(4!))
378 = (4!!)!! - 4!! + 4 - sqr(4)
379 = (4!!)!! - 4!! + 4 - int(ln(4))
380 = (4!!)!! - 4!! + 4 x int(ln(4))
381 = (4!!)!! - 4!! + 4 + int(ln(4))
382 = (4!!)!! - 4!! + 4 + sqr(4)
383 = (4!!)!! - 4!! + 4 + int(ln(4!))
384 = (4!!)!! - 4!! + 4 + 4
385 = (4!!)!! + 4 - 4 + int(ln(4))
386 = (4!!)!! + 4 - 4 + sqr(4)
387 = (4!!)!! + 4 - 4 + int(ln(4!))
388 = (4!!)!! + 4 + 4 - 4
389 = (4!!)!! + 4 + 4 - int(ln(4!))
390 = (4!!)!! + 4 + 4 - sqr(4)
391 = (4!!)!! + 4 + 4 - int(ln(4))
392 = (4!!)!! + 4 + 4 x int(ln(4!))
393 = (4!!)!! + 4 + 4 + int(ln(4))
394 = (4!!)!! + 4 + 4 + sqr(4)
395 = (4!!)!! + 4 + 4 + int(ln(4!))
396 = (4!!)!! + 4 + 4 + 4
397 = (4!!)!! + 4!! + 4 + int(ln(4))
398 = (4!!)!! + 4!! + 4 + sqr(4)
399 = (4!!)!! + 4!! + 4 + int(ln(4!))
400 = (4!!)!! + 4!! + 4!! x int(ln(4))
401 = (4!!)!! + 4!! + 4!! + int(ln(4))
402 = (4!!)!! + 4!! + 4!! + sqr(4)
403 = (4!!)!! + 4!! + 4!! + int(ln(4!))
404 = (4!!)!! + 4!! + 4!! + 4
405 = (4!!)!! + 4! - 4 + int(ln(4))
406 = (4!!)!! + 4! - 4 + sqr(4)
407 = (4!!)!! + 4! - 4 + int(ln(4!))
408 = (4!!)!! + 4! - 4 + 4
409 = (4!!)!! + 4! + 4 - int(ln(4!))
410 = (4!!)!! + 4! + 4 - sqr(4)
411 = (4!!)!! + 4! + 4 - int(ln(4))
412 = (4!!)!! + 4! + 4 x int(ln(4))
413 = (4!!)!! + 4! + 4 + int(ln(4))
414 = (4!!)!! + 4! + 4 + sqr(4)
415 = (4!!)!! + 4! + 4 + int(ln(4!))
416 = (4!!)!! + 4! + 4 + 4
417 = (4!!)!! + 4! + 4!! + int(ln(4))
418 = (4!!)!! + 4! + 4!! + sqr(4)
419 = (4!!)!! + 4! + 4!! + int(ln(4!))
420 = (4!!)!! + 4! + 4!! + 4
421 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! - int(ln(4!))
422 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! - sqr(4)
423 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! - int(ln(4))
424 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! x int(ln(4))
425 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! + int(ln(4))
426 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! + sqr(4)
427 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! + int(ln(4!))
428 = (4!!)!! + ((int(ln(4!)))!)!! - 4!! + 4
429 = (4!!)!! + ((int(ln(4!)))!)!! - 4 + int(ln(4))
430 = (4!!)!! + ((int(ln(4!)))!)!! - 4 + sqr(4)
431 = (4!!)!! + ((int(ln(4!)))!)!! - 4 + int(ln(4!))
432 = (4!!)!! + ((int(ln(4!)))!)!! - 4 + 4
433 = (4!!)!! + ((int(ln(4!)))!)!! + 4 - int(ln(4!))
434 = (4!!)!! + ((int(ln(4!)))!)!! + 4 - sqr(4)
435 = (4!!)!! + ((int(ln(4!)))!)!! + 4 - int(ln(4))
436 = (4!!)!! + ((int(ln(4!)))!)!! + 4 x int(ln(4))
437 = (4!!)!! + ((int(ln(4!)))!)!! + 4 + int(ln(4))
438 = (4!!)!! + ((int(ln(4!)))!)!! + 4 + sqr(4)
439 = (4!!)!! + ((int(ln(4!)))!)!! + 4 + int(ln(4!))
440 = 444 - 4
441 = 444 - int(ln(4!))
442 = 444 - sqr(4)
443 = 444 - int(ln(4))
444 = 444 x int(ln(4))
445 = 444 + int(ln(4))
446 = 444 + sqr(4)
447 = 444 + int(ln(4!))
448 = 444 + 4
449 = (4!!)!! + 4^int(ln(4!)) + int(ln(4))
450 = (4!!)!! + 4^int(ln(4!)) + sqr(4)
451 = (4!!)!! + 4^int(ln(4!)) + int(ln(4!))
452 = (4!!)!! + 4^int(ln(4!)) + 4
453 = (4!!)!! + S((int(ln(4!)))!,int(ln(4))) + 4
454 = (4!!)!! + 4^int(ln(4!)) + (int(ln(4!)))!
455 = (4!!)!! + S((int(ln(4!)))!,int(ln(4))) + (int(ln(4!)))!
456 = (4!!)!! + 4^int(ln(4!)) + 4!!
457 = (4!!)!! + S((int(ln(4!)))!,int(ln(4))) + 4!!
458 = S((int(ln(4!)))^sqr(4),int(ln(4))) - 4
459 = S((int(ln(4!)))^sqr(4),int(ln(4))) - int(ln(4!))
460 = S((int(ln(4!)))^sqr(4),int(ln(4))) - sqr(4)
461 = S((int(ln(4!)))^sqr(4),int(ln(4))) - int(ln(4))
462 = S((int(ln(4!)))^sqr(4),int(ln(4))) x int(ln(4))
463 = S((int(ln(4!)))^sqr(4),int(ln(4))) + int(ln(4))
464 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! x int(ln(4))
465 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + int(ln(4))
466 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + sqr(4)
467 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + int(ln(4!))
468 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + 4
469 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + int(ln((4!!)!!))
470 = (((int(ln(4!)))!)!! + int(ln((4!!)!))) x 4!! + (int(ln(4!)))!
471 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - (int(ln(4!)))^sqr(4)
472 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - 4-4
473 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - 4-int(ln(4!))
474 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - (int(ln(4!)))! x int(ln(4))
475 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - 4-int(ln(4))
476 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - sqr(4x4)
477 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - int(ln(4!)) x int(ln(4))
478 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - sqr(sqr(4x4))
479 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) - 4/4
480 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4-4
481 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4/4
482 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + sqr(sqr(4x4))
483 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + int(ln(4!)) x int(ln(4))
484 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + sqr(4x4)
485 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4+int(ln(4))
486 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + (int(ln(4!)))! x int(ln(4))
487 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4+int(ln(4!))
488 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4+4
489 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + (int(ln(4!)))^sqr(4)
490 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4+(int(ln(4!)))!
491 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + int(ln((4!!)!!))+(int(ln(4!)))!
492 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4 x int(ln(4!))
493 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4!! x int(ln((4!!)!!))
494 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4!! x (int(ln(4!)))!
495 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + int(ln((4!!)!)) + int(ln((4!!)!!))
496 = ((int(ln(4!)))!)!! x int(ln((4!!)!)) + 4x4
497 = int(ln(sqr(sqr(sqr((((int(ln(4!)))!)!!)!))))) x (4!+(int(ln(4!)))!) - int(ln(sqr(sqr((4!)!))))


NOTE:
x!! semifattoriale
S(n,k) numeri di Stirling di seconda specie
int funzione parte intera
abs valore assoluto
ln logaritmo naturale

65 = S(6,1) numero di Stirling
462 = S(9,1) numero di Stirling

1 = int(ln(4))
2 = sqr(4)
3 = int(ln(4!))
4 = 4
5 = int(ln((4!!)!!))
6 = (int(ln(4!)))!
7 = 4+int(ln(4!))
8 = 4!!
9 = (int(ln(4!)))^sqr(4)
10 = int(ln((4!!)!))

13 = int(ln(sqr(sqr((4!)!))))

17 = int(ln(sqr(sqr(sqr((((int(ln(4!)))!)!!)!)))))


24 = 4!
48 = (int(ln(4!)))!)!!
384 = (4!!)!!
40320 = (4!!)!
Yoda
2019-08-11 13:08:11 UTC
Permalink
Post by Chenickname
414 = (4!!)!! + 4! + 4 + sqr(4)
Mi sa che non sara' per niente facile ne' piccolo, perche' vedi: il 414
lo becchi in un sol colpo cosi':

int(Log(sf(sf(sf(4)))))

essendo Log() il log in base 10, che come funzione non puo' ch'essere
valida al pari del log naturale ln() (che in mat e fis s'usa scrivere
ancora log() invece di ln()) e che in ogni caso figura col simbolo log()
(minuscolo) in tutte le calcolatrici ciao
--
Yoda
Yoda
2019-08-11 13:18:05 UTC
Permalink
Post by Yoda
int(Log(sf(sf(sf(4)))))
Scusa sf() e' !!, ho incollato dalla riga di comando di bc, per la quale
ho fatto la funzione chiamandola sf(), eccola ciao

/* semifattoriale recorsivo */
define sf(x) {
if (x<=1) return (1);
return (x * sf(x-2));
}
--
Yoda
Maurizio Frigeni
2019-08-14 14:11:56 UTC
Permalink
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
La pagina di Wikipedia dedicata al puzzle
(https://en.wikipedia.org/wiki/Four_fours)
fa notare che, se si ammette il logaritmo fra i simboli da usare, allora
si può trovare qualunque numero così:

n = -√(4) ln[ln(√√√√...√4)/ln(4)]/ln(4)

dove √ è il simbolo di radice quadrata (spero che compaia giusto) e ad
argomento del ln ci sono n radici quadrate annidate.

M.
--
Per rispondermi via e-mail togli l'ovvio.
Chenickname
2019-08-16 18:43:57 UTC
Permalink
Post by Maurizio Frigeni
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
La pagina di Wikipedia dedicata al puzzle
(https://en.wikipedia.org/wiki/Four_fours)
fa notare che, se si ammette il logaritmo fra i simboli da usare, allora
n = -√(4) ln[ln(√√√√...√4)/ln(4)]/ln(4)
dove √ è il simbolo di radice quadrata (spero che compaia giusto) e ad
argomento del ln ci sono n radici quadrate annidate.
M.
--
Per rispondermi via e-mail togli l'ovvio.
Grazie!
Almeno sospendo la ricerca! :-)
Forse potrebbe restare in piedi la domanda di qual e' il primo intero non rappresentabile da quattro 4 senza usare i logaritmi, oppure usando ben determinate operazioni matematiche.
Yoda
2019-08-16 19:13:46 UTC
Permalink
Il giorno mercoledì 14 agosto 2019 16:11:57 UTC+2,
Post by Maurizio Frigeni
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
La pagina di Wikipedia dedicata al puzzle
(https://en.wikipedia.org/wiki/Four_fours)
fa notare che, se si ammette il logaritmo fra i simboli da usare, allora
n = -√(4) ln[ln(√√√√...√4)/ln(4)]/ln(4)
dove √ è il simbolo di radice quadrata (spero che compaia giusto) e ad
argomento del ln ci sono n radici quadrate annidate.
Da me non si vede, ma sono in console a caratteri, sulla GUI si vede
certamente perche' e' un carattere utf8 (aschi esteso 8730 decimale).
Grazie!
Almeno sospendo la ricerca! :-)
Si', l'avevo anche 1/2 intuito anch'io, quando ti dissi che col log
potevi beccare il 414 in un colpo solo, ora Maurizio l'ha dimostrato.
Forse potrebbe restare in piedi la domanda di qual e' il primo intero
non rappresentabile da quattro 4 senza usare i logaritmi, oppure usando
ben determinate operazioni matematiche.
con le 4 aritmetiche forse diventa banale, magari invece aggiungendo
le potenze ad esponente intero? ciao
--
Yoda
Chenickname
2019-08-16 19:20:47 UTC
Permalink
Post by Chenickname
Post by Maurizio Frigeni
Post by Chenickname
Quale sara' il primo intero non rappresentabile da quattro 4?
La pagina di Wikipedia dedicata al puzzle
(https://en.wikipedia.org/wiki/Four_fours)
fa notare che, se si ammette il logaritmo fra i simboli da usare, allora
n = -√(4) ln[ln(√√√√...√4)/ln(4)]/ln(4)
dove √ è il simbolo di radice quadrata (spero che compaia giusto) e ad
argomento del ln ci sono n radici quadrate annidate.
M.
--
Per rispondermi via e-mail togli l'ovvio.
Grazie!
Almeno sospendo la ricerca! :-)
Forse potrebbe restare in piedi la domanda di qual e' il primo intero non rappresentabile da quattro 4 senza usare i logaritmi, oppure usando ben determinate operazioni matematiche.
33 = 4!+!4x4/4
34 = 4!+4+4+sqr(4)
35 = 4!+4/sqr(4)+!4
36 = 44-4-4
37 = 44-!4+sqr(4)
38 = 44-4-sqr(4)
39 = gamma(4) x gamma(4) + gamma(4) / sqr(4)
40 = 44-sqr(4)-sqr(4)
41 = gamma(4) x gamma(4) + sqr(4) + sqr(!4)
42 = 44-4/sqr(4)
43 = 44-4/4
44 = 44+4-4
45 = 44+4/4
46 = 44+4/sqr(4)
47 = gamma(4) x gamma(4) + sqr(4) + !4
48 = gamma(4) x 4!! x 4/4
49 = gamma(4) x 4!! + 4/4
...

La tentazione è di nuovo forte. :-)

Continua a leggere su narkive:
Loading...