A212648 Minimal m >= 0 such that (2*n-1)!! - 2^m is prime.

0, 1, 1, 2, 2, 2, 1, 1, 1, 6, 9, 2, 6, 6, 8, 16, 2, 15, 6, 3, 3, 5, 7, 26, 1, 8, 16, 18, 7, 14, 12, 9, 5, 14, 8, 1, 32, 7, 2, 2, 3, 53, 8, 1, 3, 10, 10, 20, 8, 25, 20, 2, 23, 7, 13, 21, 87, 16, 76, 35, 30, 18, 12, 7, 1, 117, 36, 40, 57, 25, 3, 5, 47, 62

Offset: 2

Author

Vladimir Shevelev, Feb 14 2013

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A212281, A212282, A212321, A212636, A212637.

Programs

Maple

f:= proc(n) local m,t;
  t:= doublefactorial(2*n-1);
  for m from 0 do
    if isprime(t - 2^m) then return m fi
  od
end proc:
map(f, [$2..100]); # Robert Israel, Jul 20 2023

Mathematica

a[n_] := Block[{f=(2*n-1)!!, m=0}, While[! PrimeQ[f - 2^m], m++]; m]; a /@ Range[2, 75] (* Giovanni Resta, Feb 14 2013 *)

Extensions

a(8)-a(75) from Giovanni Resta, Feb 14 2013