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A111019
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Indices of Catalan numbers that are == 1 mod 3 (cf. A000108).
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1
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1, 11, 12, 13, 29, 30, 31, 35, 36, 37, 83, 84, 85, 89, 90, 91, 107, 108, 109, 119, 120, 121, 245, 246, 247, 251, 252, 253, 269, 270, 271, 281, 282, 283, 323, 324, 325, 335, 336, 337, 353, 354, 355, 359, 360, 361, 731, 732, 733, 737, 738, 739, 755
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OFFSET
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1,2
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LINKS
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FORMULA
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a(3k) = a(3k-1)+1 and a(3k+1) = a(3k-1)+2 for k >= 1. - Robert Israel, Jun 30 2020
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MAPLE
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filter:= proc(n) local L1, L2, L3;
L1:= convert(2*n, base, 3);
L2:= convert(n, base, 3);
L3:= convert(n-1, base, 3);
mul(binomial(L1[i], L2[i]), i=1..nops(L2)) - mul(binomial(L1[i], L3[i]), i=1..nops(L3)) mod 3 = 1
end proc:
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MATHEMATICA
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Flatten[Position[CatalanNumber[Range[1000]], _?(Mod[#, 3]==1&)]] (* Harvey P. Dale, Jun 19 2014 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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