This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156301 #34 Aug 01 2025 00:14:03
%S A156301 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,
%T A156301 18,19,19,20,21,21,22,23,23,24,24,25,26,26,27,28,28,29,30,30,31,31,32,
%U A156301 33,33,34,35,35,36,36,37,38,38,39,40,40,41,42,42,43,43,44,45,45,46,47
%N A156301 a(n) = ceiling( n * log_3(2) ) = ceiling(n * 0.6309297535714574371...).
%C A156301 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.
%H A156301 Reinhard Zumkeller, <a href="/A156301/b156301.txt">Table of n, a(n) for n = 0..10000</a>
%H A156301 Li an-Ping, <a href="http://arxiv.org/abs/0902.0841">A note on the counterfeit coins problem</a>, arXiv:0902.0841 [math.CO], 2009-2010.
%H A156301 A. Gorman-Huang and E. Marks, <a href="http://girlsangle.org/page/bulletin-archive/GABv18n05E.pdf">Approximating Powers of 2 Using Powers of 3 and Break Point Rounding</a>, Girls' Angle Bulletin, Vol. 18, No. 5 (2025), 8-10.
%p A156301 seq(ceil(n*log[3](2)),n=0..120) ; # _R. J. Mathar_, Mar 14 2009
%t A156301 With[{c=Log[3,2]},Ceiling[c*Range[0,80]]] (* _Harvey P. Dale_, Aug 07 2015 *)
%o A156301 (Haskell)
%o A156301 a156301 = ceiling . (* logBase 3 2) . fromIntegral
%o A156301 -- _Reinhard Zumkeller_, Jul 03 2015
%o A156301 (Python)
%o A156301 from operator import sub
%o A156301 from sympy import integer_log
%o A156301 def A156301(n): return sub(*integer_log(1<<n,3))+1 # _Chai Wah Wu_, Oct 09 2024
%Y A156301 Cf. A020915, A102525. - _R. J. Mathar_, Feb 19 2009
%Y A156301 Cf. A136409.
%K A156301 easy,nonn
%O A156301 0,3
%A A156301 _Jonathan Vos Post_, Feb 07 2009
%E A156301 More terms from _R. J. Mathar_, Mar 14 2009
%E A156301 Edited by _N. J. A. Sloane_, May 23 2009 at the suggestion of _Hagen von Eitzen_