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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
Ignoring the first term, first differences of A066343. - Andrew Woods, Jun 10 2013
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
First differences of A067497.
Sequence in context: A026858 A188885 A362330 * A048853 A303701 A179845
KEYWORD
base,nonn
AUTHOR
Tanya Khovanova, May 28 2007
STATUS
approved

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Last modified February 27 10:59 EST 2024. Contains 370378 sequences. (Running on oeis4.)