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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

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

Crossrefs

Cf. A055253, A055254.

Cf. A000079, A055642.

See A125117 for the sequence of first differences.

Programs

Magma

[#Intseq(2^n): n in [0..100] ]; // Vincenzo Librandi, Jun 23 2015

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 *)

PARI

A034887(n)=n*log(2)\log(10)+1 \\ or: { a(n)=#digits(1<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

Formula

a(n) = floor(n*log_10(2)) + 1. E.g., a(10)=4 because 2^10 = 1024 and floor(10*log_10(2)) + 1 = 3 + 1 = 4. - Jaap Spies, Dec 11 2003

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