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A125117 First differences of A034887.

%I A125117 #23 Jun 08 2024 09:34:11
%S A125117 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,
%T A125117 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,
%U A125117 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
%N A125117 First differences of A034887.
%C A125117 This sequence is not periodic because log(2)/log(10) is an irrational number. - _T. D. Noe_, Jan 10 2007
%C A125117 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
%H A125117 Paolo Xausa, <a href="/A125117/b125117.txt">Table of n, a(n) for n = 0..10000</a>
%F A125117 a(n) = number_of_digits{2^(n+1)} - number_of_digits{2^(n)} with n>=0.
%e A125117 a(1)=0 because 2^(1+1)=4 (one digit) 2^1=2 (one digit) and the difference is 0.
%e A125117 a(3)=1 because 2^(3+1)=16 (two digits) 2^(3)=8 (one digit) and the difference is 1.
%p A125117 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);
%t A125117 Differences[IntegerLength[2^Range[0, 100]]] (* _Paolo Xausa_, Jun 08 2024 *)
%o A125117 (PARI) a(n)=logint(2^(n+1),10)-logint(2^n,10) \\ _Charles R Greathouse IV_, Oct 19 2016
%Y A125117 Cf. A034887, A144597, A276397.
%K A125117 easy,nonn,base
%O A125117 0,1
%A A125117 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jan 10 2007