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A212636 Minimal m >= 1 such that floor((2*n - 1)!!/m) - 2 is prime.

%I A212636 #26 May 24 2025 09:42:42
%S A212636 1,1,3,3,8,1,1,1,5,7,19,7,5,15,7,17,5,3,9,11,63,9,5,1,53,27,51,11,3,
%T A212636 11,13,15,17,35,1,17,21,13,139,61,3,13,1,7,147,23,123,47,41,35,11,39,
%U A212636 69,21,123,29,27,49,3,9,37,171,57,1,31,37,5,61,27,31,53
%N A212636 Minimal m >= 1 such that floor((2*n - 1)!!/m) - 2 is prime.
%e A212636 (2*6-1)!! = 11!! = 11 * 9 * 7 * 5 * 3 * 1 = 10395. Floor(10395/1) - 2 = 10395 - 2 = 10393 =  19 * 547 is not prime, and floor(10395/2) - 2 = 5197 - 2 = 5195 = 5 * 1039 is not prime, but floor(10395/3) - 2 = 3465 - 2 = 3463 is prime, so a(6) = 3.
%p A212636 a:= proc(n) local m;
%p A212636       for m while not isprime(iquo(doublefactorial(2*n-1), m)-2)
%p A212636       do od; m
%p A212636     end:
%p A212636 seq(a(n), n=3..70);  #  _Alois P. Heinz_, Feb 18 2013
%t A212636 a[n_] := Module[{m}, For[m = 1, True, m++, If[PrimeQ[Floor[(2n-1)!!/m]-2], Return[m]]]];
%t A212636 Table[a[n], {n, 3, 73}] (* _Jean-François Alcover_, May 24 2025 *)
%Y A212636 Cf. A212281, A212282, A212321.
%K A212636 nonn
%O A212636 3,3
%A A212636 _Vladimir Shevelev_, Feb 14 2013
%E A212636 More terms from _Alois P. Heinz_, Feb 18 2013