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 A111018 #39 Sep 08 2022 08:45:20 %S A111018 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 A111018 47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69, %U A111018 70,71,72,73,74,75,76,77,78,79,86,87,88,95,96,97,98,99,100 %N A111018 Indices of Catalan numbers that are divisible by 3. %C A111018 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 A111018 The asymptotic density of this sequence is 1 (Burns, 2016). - _Amiram Eldar_, Jan 26 2021 %H A111018 G. C. Greubel, <a href="/A111018/b111018.txt">Table of n, a(n) for n = 1..1000</a> %H A111018 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 A111018 Flatten[Position[CatalanNumber[Range[100]],_?(Divisible[#,3]&)]] (* _Harvey P. Dale_, Oct 25 2011 *) %t A111018 Select[Range@100, Divisible[CatalanNumber@#,3]&] (* _Vladimir Reshetnikov_, Nov 06 2015 *) %o A111018 (PARI) for(n=0, 1e3, if(binomial(2*n, n)/(n+1) % 3 == 0, print1(n, ", "))) \\ _Altug Alkan_, Dec 02 2015 %o A111018 (Magma) [n: n in [1..200] | Binomial(2*n, n) div (n+1) mod 3 eq 0]; // _Vincenzo Librandi_, Dec 03 2015 %Y A111018 Cf. A000108. %Y A111018 Cf. A085296, A265100, A265104. %K A111018 nonn %O A111018 1,1 %A A111018 _Robert G. Wilson v_, Sep 09 2005