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A111018
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Indices of Catalan numbers that are divisible by 3.
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2
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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
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Flatten[Position[CatalanNumber[Range[100]], _?(Divisible[#, 3]&)]] (* Harvey P. Dale, Oct 25 2011 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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