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%I #39 Sep 08 2022 08:45:20
%S 5,6,7,14,15,16,17,18,19,20,21,22,23,24,25,32,33,34,41,42,43,44,45,46,
%T 47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,
%U 70,71,72,73,74,75,76,77,78,79,86,87,88,95,96,97,98,99,100
%N Indices of Catalan numbers that are divisible by 3.
%C Conjecture: The sequence contains all numbers n such that n and n+1 are both in the sequence A074940, or, equivalently, such that neither n nor n+1 is in the sequence A005836. - _L. Edson Jeffery_, Dec 02 2015
%C The asymptotic density of this sequence is 1 (Burns, 2016). - _Amiram Eldar_, Jan 26 2021
%H G. C. Greubel, <a href="/A111018/b111018.txt">Table of n, a(n) for n = 1..1000</a>
%H Rob Burns, <a href="https://arxiv.org/abs/1611.03705">Asymptotic density of Catalan numbers modulo 3 and powers of 2</a>, arXiv:1611.03705 [math.NT], 2016.
%t Flatten[Position[CatalanNumber[Range[100]],_?(Divisible[#,3]&)]] (* _Harvey P. Dale_, Oct 25 2011 *)
%t Select[Range@100, Divisible[CatalanNumber@#,3]&] (* _Vladimir Reshetnikov_, Nov 06 2015 *)
%o (PARI) for(n=0, 1e3, if(binomial(2*n, n)/(n+1) % 3 == 0, print1(n, ", "))) \\ _Altug Alkan_, Dec 02 2015
%o (Magma) [n: n in [1..200] | Binomial(2*n, n) div (n+1) mod 3 eq 0]; // _Vincenzo Librandi_, Dec 03 2015
%Y Cf. A000108.
%Y Cf. A085296, A265100, A265104.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 09 2005
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