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 A083096 #29 Jan 15 2025 10:59:39
%S A083096 0,12,30,36,84,90,108,120,246,252,270,282,324,336,354,360,732,738,756,
%T A083096 768,810,822,840,846,972,984,1002,1008,1056,1062,1080,1092,2190,2196,
%U A083096 2214,2226,2268,2280,2298,2304,2430,2442,2460,2466,2514,2520,2538,2550
%N A083096 Numbers k such that 3 divides Sum_{j=1..k} binomial(2*j,j).
%C A083096 Apparently a(n)/3 (mod 3) = A010060(n-1), the Thue-Morse sequence.
%H A083096 Hugo Pfoertner, <a href="/A083096/b083096.txt">Table of n, a(n) for n = 1..8192</a>
%F A083096 It appears that sequence gives k such that the coefficient of x^k equals 1 in Product_{j>=1} 1-x^(3^j).
%t A083096 Reap[ For[n = 0, n <= 3000, n = n + 3, If[ Divisible[ Sum[ Binomial[2 k, k], {k, 1, n}], 3], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Jul 01 2013 *)
%t A083096 Join[{0},Position[Accumulate[Table[Binomial[2k,k],{k,2600}]],_?( Divisible[ #,3]&)]//Flatten] (* _Harvey P. Dale_, Mar 14 2020 *)
%Y A083096 Cf. A066796, A083097, A081601.
%K A083096 nonn,easy
%O A083096 1,2
%A A083096 _Benoit Cloitre_, Apr 22 2003