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

%I A212648 #21 Jul 24 2023 10:17:45
%S A212648 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,
%T A212648 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,
%U A212648 76,35,30,18,12,7,1,117,36,40,57,25,3,5,47,62
%N A212648 Minimal m >= 0 such that (2*n-1)!! - 2^m is prime.
%H A212648 Robert Israel, <a href="/A212648/b212648.txt">Table of n, a(n) for n = 2..1000</a>
%p A212648 f:= proc(n) local m,t;
%p A212648   t:= doublefactorial(2*n-1);
%p A212648   for m from 0 do
%p A212648     if isprime(t - 2^m) then return m fi
%p A212648   od
%p A212648 end proc:
%p A212648 map(f, [$2..100]); # _Robert Israel_, Jul 20 2023
%t A212648 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 *)
%Y A212648 Cf. A212281, A212282, A212321, A212636, A212637.
%K A212648 nonn
%O A212648 2,4
%A A212648 _Vladimir Shevelev_, Feb 14 2013
%E A212648 a(8)-a(75) from _Giovanni Resta_, Feb 14 2013