A131381 -id:A131381 - cp's OEIS frontend

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

Offset: 1

Robert G. Wilson v, May 11 2004

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

Robert Israel, Table of n, a(n) for n = 1..10000
Robert Israel, Characterization of A094453

Cf. A000108, A000984, A005836, A094575, A094576, A131381, A191107.

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])
  fi fi
end proc:select(filter, [$1..1000]); # Robert Israel, Nov 17 2024

Select[ Range[735], Mod[Binomial[2#, # ], (# + 2)] != 0 &]

cp's OEIS Frontend

A094453 Numbers k such that binomial(2*k, k)/(k+2) is not an integer.

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