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 A081601 #39 Jun 29 2025 10:58:43
%S A081601 0,3,9,12,27,30,36,39,81,84,90,93,108,111,117,120,243,246,252,255,270,
%T A081601 273,279,282,324,327,333,336,351,354,360,363,729,732,738,741,756,759,
%U A081601 765,768,810,813,819,822,837,840,846,849,972,975,981,984,999,1002,1008,1011
%N A081601 Numbers m such that 3 does not divide Sum_{k=0..m} binomial(2k,k) = A006134(m).
%C A081601 Apparently a(n)/3 mod 2 = A010060(n-1), the Thue-Morse sequence.
%C A081601 a(n+1) is the smallest number with exactly n+1 partitions into distinct powers of 2 or of 3: A131996(a(n+1)) = n+1 and A131996(m) < n+1 for m < a(n+1). - _Reinhard Zumkeller_, Aug 06 2007
%H A081601 Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H A081601 Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F A081601 Apparently a(n) = 3*A005836(n).
%F A081601 G.f.: (x/(1 - x))*Sum_{k>=0} 3^(k+1)*x^(2^k)/(1 + x^(2^k)) (conjecture). - _Ilya Gutkovskiy_, Jul 23 2017
%e A081601 For n=0, A006134(0) = 1, hence 0 is a term.
%t A081601 Select[Range[0, 1020], Mod[Sum[Binomial[2 k, k], {k, 0, #}], 3] != 0 &] (* _Michael De Vlieger_, Nov 28 2015 *)
%o A081601 (PARI) for(n=0, 1e3, if(sum(k=0, n, binomial(2*k, k)) % 3 > 0, print1(n,", "))) \\ _Altug Alkan_, Nov 26 2015
%Y A081601 Cf. A005836, A006134, A006996, A010060, A083096, A131996.
%Y A081601 Equals A089118(n-2) + 1, n > 1.
%K A081601 easy,nonn
%O A081601 1,2
%A A081601 _Benoit Cloitre_, Apr 22 2003
%E A081601 Zero prepended to the sequence and formulas modified accordingly by _L. Edson Jeffery_, Nov 25 2015