

A129344


a(n) is the number of powers of 2 that have n decimal digits.


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, 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
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OFFSET

1,1


COMMENTS

Ignoring the first term, first differences of A066343. [Andrew Woods, Jun 10 2013]


LINKS

Table of n, a(n) for n=1..93.


FORMULA

For n>1, a(n) = floor(n*L)floor((n1)*L) where L = log(10)/log(2). [Andrew Woods, Jun 10 2013]


EXAMPLE

a(1) is 4 because there are 4 onedigit 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}]


PROG

(PARI) a(n) = my(k=0, i=0); while(#Str(2^k)!=n, k++); while(#Str(2^k)==n, i++; k++); i \\ Felix FrÃ¶hlich, Jan 19 2016


CROSSREFS

First differences of A067497. Also n such that 1 is the first digit of 2^n (cf. A000079).
Sequence in context: A281705 A026858 A188885 * A048853 A179845 A180217
Adjacent sequences: A129341 A129342 A129343 * A129345 A129346 A129347


KEYWORD

base,nonn


AUTHOR

Tanya Khovanova, May 28 2007


STATUS

approved



