A034888 Number of digits in 3^n.

1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 32, 33, 33

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000244 (powers of 3), A055642 (number of digits of n).

Programs

Magma

[#Intseq(3^n): n in [0..100] ]; // Vincenzo Librandi, Jun 23 2015

Maple

seq(floor(n*ln(3)/ln(10))+1, n=0..100);

Mathematica

Table[Length[IntegerDigits[3^n]], {n, 0, 100}] (* T. D. Noe, Mar 20 2012 *)
IntegerLength[3^Range[0,70]] (* Harvey P. Dale, Jan 28 2015 *)

PARI

a(n)=#Str(3^n) \\ Charles R Greathouse IV, Jul 03 2013

Python

def a(n): return len(str(3**n))
print([a(n) for n in range(70)]) # Michael S. Branicky, Dec 23 2022

Formula

a(n) = floor(n*log(3)/log(10)) + 1. E.g., a(10)=5 because 3^10 = 59049 and floor(10*log(3)/log(10)) + 1 = 4 + 1 = 5. - Jaap Spies, Dec 15 2003

a(n) = A055642(3^n) = A055642(A000244(n)). - Michel Marcus, Jun 23 2015