A111018 Indices of Catalan numbers that are divisible by 3.

5, 6, 7, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 86, 87, 88, 95, 96, 97, 98, 99, 100

Offset

1,1

Comments

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

The asymptotic density of this sequence is 1 (Burns, 2016). - Amiram Eldar, Jan 26 2021

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Rob Burns, Asymptotic density of Catalan numbers modulo 3 and powers of 2, arXiv:1611.03705 [math.NT], 2016.

Mathematica

Flatten[Position[CatalanNumber[Range[100]], _?(Divisible[#, 3]&)]] (* Harvey P. Dale, Oct 25 2011 *)
Select[Range@100, Divisible[CatalanNumber@#, 3]&] (* Vladimir Reshetnikov, Nov 06 2015 *)

Prog

(PARI) for(n=0, 1e3, if(binomial(2*n, n)/(n+1) % 3 == 0, print1(n, ", "))) \\ Altug Alkan, Dec 02 2015
(Magma) [n: n in [1..200] | Binomial(2*n, n) div (n+1) mod 3 eq 0]; // Vincenzo Librandi, Dec 03 2015

Crossrefs

Cf. A000108.

Cf. A085296, A265100, A265104.

Sequence in context: A031029 A134985 A371029 * A326132 A342630 A347807

Adjacent sequences: A111015 A111016 A111017 * A111019 A111020 A111021

Keyword

nonn

Author

Robert G. Wilson v, Sep 09 2005

Status

approved