A094453 - OEIS

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A094453

Numbers k such that binomial(2*k, k)/(k+2) is not an integer.

1, 2, 4, 6, 7, 10, 13, 14, 25, 28, 30, 31, 34, 37, 40, 62, 79, 82, 85, 88, 91, 94, 106, 109, 112, 115, 118, 121, 126, 241, 244, 247, 250, 253, 254, 256, 268, 271, 274, 277, 280, 283, 322, 325, 328, 331, 334, 337, 349, 352, 355, 358, 361, 364, 510, 727, 730, 733

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OFFSET

1,2

COMMENTS

A191107 is a subsequence as the relevant terms of A000984 are not divisible by 3 (see the comments in A005836 and A191107). - Peter Munn, Aug 14 2023

Numbers k such that either k + 2 is a power of 2, or k + 2 is divisible by 3 and none of the base-3 digits of k + 2 are 2 except possibly the second-last. See link for proof. Thus the sequence is the union of the positive terms of A00984 and of 9*k-2, 9*k + 1 and 9*k + 4 for k in A005836. - Robert Israel, Nov 17 2024

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Robert Israel, Characterization of A094453

MAPLE

filter:= proc(n) local r, L;

r:= n+2;

if r = 2^padic:-ordp(r, 2) then true

else

if r mod 3 <> 0 then false

else

L:= convert(r, base, 3);

not member(2, L[3..-1])