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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 21 10:04 EDT 2021. Contains 343148 sequences. (Running on oeis4.)