|
|
A129344
|
|
a(n) is the number of powers of 2 that have n decimal digits.
|
|
4
|
|
|
4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
For n>1, a(n) = floor(n*L)-floor((n-1)*L) where L = log(10)/log(2). - Andrew Woods, Jun 10 2013
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log_2(10) (A020862). - Amiram Eldar, Apr 09 2021
|
|
EXAMPLE
|
a(1) is 4 because there are 4 one-digit powers of 2: 1, 2, 4, 8.
|
|
MATHEMATICA
|
Table[Transpose[ Select[Table[{n, 2^n}, {n, 0, 310}], IntegerDigits[ #[[2]]][[1]] == 1 &]][[1]][[k]] - Transpose[ Select[Table[{n, 2^n}, {n, 0, 310}], IntegerDigits[ #[[2]]][[1]] == 1 &]][[1]][[k - 1]], {k, 2, 94}]
Join[{4}, Differences @ Table[Floor[n*Log2[10]], {n, 100}]] (* Amiram Eldar, Apr 09 2021 *)
|
|
PROG
|
(PARI) a(n) = my(k=0, i=0); while(#Str(2^k)!=n, k++); while(#Str(2^k)==n, i++; k++); i \\ Felix Fröhlich, Jan 19 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|