

A111018


Indices of Catalan numbers that are divisible by 3.


2



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
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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: A067531 A031029 A134985 * A326132 A342630 A161925
Adjacent sequences: A111015 A111016 A111017 * A111019 A111020 A111021


KEYWORD

nonn,changed


AUTHOR

Robert G. Wilson v, Sep 09 2005


STATUS

approved



