A094453 - OEIS

%I #20 Nov 18 2024 07:33:19

%S 1,2,4,6,7,10,13,14,25,28,30,31,34,37,40,62,79,82,85,88,91,94,106,109,

%T 112,115,118,121,126,241,244,247,250,253,254,256,268,271,274,277,280,

%U 283,322,325,328,331,334,337,349,352,355,358,361,364,510,727,730,733

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

%C 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

%C 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

%H Robert Israel, <a href="/A094453/b094453.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert Israel, <a href="/A094453/a094453.pdf">Characterization of A094453</a>

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

%p   r:= n+2;

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

%p   else

%p     if r mod 3 <> 0 then false

%p     else

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

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

%p   fi fi

%p end proc:select(filter, [$1..1000]); # _Robert Israel_, Nov 17 2024

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

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

%K nonn,look

%O 1,2

%A _Robert G. Wilson v_, May 11 2004