A034887 Number of digits in 2^n.

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, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22

Offset

0,5

Comments

The sequence consists of the positive integers, each appearing 3 or 4 times. - M. F. Hasler, Oct 08 2016

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Mersenne Number

Formula

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

a(n) = A055642(2^n) = A055642(A000079(n)).

Maple

seq(floor(n*ln(2)/ln(10))+1, n=0..100); # Jaap Spies, Dec 11 2003

Mathematica

Table[Length[IntegerDigits[2^n]], {n, 0, 100}] (* T. D. Noe, Feb 11 2013 *)
IntegerLength[2^Range[0, 80]] (* Harvey P. Dale, Jul 28 2017 *)

Prog

(Magma) [#Intseq(2^n): n in [0..100] ]; // Vincenzo Librandi, Jun 23 2015
(PARI) A034887(n)=n*log(2)\log(10)+1 \\ or: { a(n)=#digits(1<<n) }. - M. F. Hasler, Oct 08 2016
(Python)
def a(n): return len(str(1 << n))
print([a(n) for n in range(73)]) # Michael S. Branicky, Dec 23 2022

Crossrefs

Cf. A055253, A055254.

Cf. A000079, A055642.

See A125117 for the sequence of first differences.

Sequence in context: A319951 A222642 A081832 * A192543 A082964 A285524

Adjacent sequences: A034884 A034885 A034886 * A034888 A034889 A034890

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved