A156301 a(n) = ceiling( n * log_3(2) ) = ceiling(n * 0.6309297535714574371...).

0, 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

Jonathan Vos Post, Feb 07 2009

Keywords

• easy
• nonn

Comments

a(n) is the unique k such that 1/2 <= 3^a(n)/2^(n+1) < 3/2. Equality occurs iff n = 0. See Gorman-Huang and Marks.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Li an-Ping, A note on the counterfeit coins problem, arXiv:0902.0841 [math.CO], 2009-2010.
• A. Gorman-Huang and E. Marks, Approximating Powers of 2 Using Powers of 3 and Break Point Rounding, Girls' Angle Bulletin, Vol. 18, No. 5 (2025), 8-10.

Crossrefs

Cf. A020915, A102525. - R. J. Mathar, Feb 19 2009

Cf. A136409.

Programs

Haskell

a156301 = ceiling . (* logBase 3 2) . fromIntegral
-- Reinhard Zumkeller, Jul 03 2015

Maple

seq(ceil(n*log[3](2)),n=0..120) ; # R. J. Mathar, Mar 14 2009

Mathematica

With[{c=Log[3,2]},Ceiling[c*Range[0,80]]] (* Harvey P. Dale, Aug 07 2015 *)

Python

from operator import sub
from sympy import integer_log
def A156301(n): return sub(*integer_log(1<Chai Wah Wu, Oct 09 2024

Extensions

More terms from R. J. Mathar, Mar 14 2009

Edited by N. J. A. Sloane, May 23 2009 at the suggestion of Hagen von Eitzen