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%I #37 Dec 23 2022 17:25:46
%S 1,1,1,1,2,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,7,7,8,8,8,9,9,9,10,10,10,
%T 10,11,11,11,12,12,12,13,13,13,13,14,14,14,15,15,15,16,16,16,16,17,17,
%U 17,18,18,18,19,19,19,19,20,20,20,21,21,21,22,22,22
%N Number of digits in 2^n.
%C The sequence consists of the positive integers, each appearing 3 or 4 times. - _M. F. Hasler_, Oct 08 2016
%H T. D. Noe, <a href="/A034887/b034887.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MersenneNumber.html">Mersenne Number</a>
%F a(n) = floor(n*log(2)/log(10)) + 1. E.g., a(10)=4 because 2^10 = 1024 and floor(10*log(2)/log(10) + 1 = 3 + 1 = 4. - _Jaap Spies_, Dec 11 2003
%F a(n) = A055642(2^n) = A055642(A000079(n)).
%p seq(floor(n*ln(2)/ln(10))+1, n=0..100); # _Jaap Spies_, Dec 11 2003
%t Table[Length[IntegerDigits[2^n]], {n, 0, 100}] (* _T. D. Noe_, Feb 11 2013 *)
%t IntegerLength[2^Range[0,80]] (* _Harvey P. Dale_, Jul 28 2017 *)
%o (Magma) [#Intseq(2^n): n in [0..100] ]; // _Vincenzo Librandi_, Jun 23 2015
%o (PARI) A034887(n)=n*log(2)\log(10)+1 \\ or: { a(n)=#digits(1<<n) }. - _M. F. Hasler_, Oct 08 2016
%o (Python)
%o def a(n): return len(str(1 << n))
%o print([a(n) for n in range(73)]) # _Michael S. Branicky_, Dec 23 2022
%Y Cf. A055253, A055254.
%Y Cf. A000079, A055642.
%Y See A125117 for the sequence of first differences.
%K nonn,base,easy
%O 0,5
%A _N. J. A. Sloane_
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