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

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 10 2007

Keywords

• easy
• nonn
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A034887, A144597, A276397.

Programs

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 *)

PARI

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

Formula

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