A020915 Number of digits in base-3 representation of 2^n.

1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45, 46, 47

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy
• nice

Comments

For n > 0, first differences of A022331. - Michel Marcus, Oct 03 2013

Links

• William A. Tedeschi, Table of n, a(n) for n = 0..10000
• Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x+1 function, arXiv:1709.03385 [math.GM], 2017.

Crossrefs

Cf. A007089, A020914, A076227, A081604, A000079.

Cf. A022331, A102525, A136409.

Cf. A022924 (first differences).

Programs

Haskell

a020915 = a081604 . a000079  -- Reinhard Zumkeller, Mar 28 2015

Magma

[Round(1+Floor(n*(Log(2))/Log(3))): n in [0..80]]; // Vincenzo Librandi, Dec 05 2015

Mathematica

Table[Length[IntegerDigits[2^n,3]],{n,0,80}] (* Harvey P. Dale, May 02 2012 *)
Table[1 + Floor[n*Log[3, 2]], {n, 0, 73}] (* L. Edson Jeffery, Dec 04 2015 *)
IntegerLength[2^Range[0,80],3] (* Harvey P. Dale, Nov 17 2022 *)

PARI

a(n)=logint(2^n,3)+1 \\ Charles R Greathouse IV, Sep 02 2015

Formula

a(n) = 1 + floor(n*log_3(2)) = 1 + floor(n*A102525) = 1 + A136409(n). - R. J. Mathar, May 23 2009

a(n) = A081604(A000079(n)). - Reinhard Zumkeller, Jul 12 2011

a(A020914(n)) = n + 1. - Reinhard Zumkeller, Mar 28 2015

Extensions

More terms from James Sellers