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

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Sep 09 2005

STATUS

approved