A125117 First differences of A034887.

0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0

Offset

0,1

Comments

This sequence is not periodic because log(2)/log(10) is an irrational number. - T. D. Noe, Jan 10 2007

The sequence consists only of 0's and 1's. Sequence A276397 (with a 0 prefixed) is similar but differs from a(42) on. Sequence A144597 differs only from a(102) on. - M. F. Hasler, Oct 07 2016

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

a(n) = number_of_digits{2^(n+1)} - number_of_digits{2^(n)} with n>=0.

Example

a(1)=0 because 2^(1+1)=4 (one digit) 2^1=2 (one digit) and the difference is 0.
a(3)=1 because 2^(3+1)=16 (two digits) 2^(3)=8 (one digit) and the difference is 1.

Maple

P:=proc(n) local i, j, k, w, old; k:=2; for i from 1 by 1 to n do j:=k^i; w:=0; while j>0 do w:=w+1; j:=trunc(j/10); od; if i>1 then print(w-old); old:=w; else old:=w; fi; od; end: P(1000);

Mathematica

Differences[IntegerLength[2^Range[0, 100]]] (* Paolo Xausa, Jun 08 2024 *)

Prog

(PARI) a(n)=logint(2^(n+1), 10)-logint(2^n, 10) \\ Charles R Greathouse IV, Oct 19 2016

Crossrefs

Cf. A034887, A144597, A276397.

Sequence in context: A072786 A320926 A144597 * A144603 A163581 A100283

Adjacent sequences: A125114 A125115 A125116 * A125118 A125119 A125120

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 10 2007

Status

approved