A202449 - OEIS

%I #15 Aug 09 2015 01:04:12

%S 3,2,1,1,2,1,4,1,2,3,2,3,2,6,16,1,6,7,6,6,6,3,26,3,2,1,16,3,8,8,4,15,

%T 16,3,2,6,4,6,14,9,38,19,6,8,28,2,32,43,44,4,24,8,8,5,20,2,62,11,4,26,

%U 10,10,16,1,72,13,10,2,2,4,2,23,18,3,32,12,132

%N Least k such that k*n!! - 1 is a prime number.

%C Using Xylouris' version of Linnik's theorem, a(n) << (n/e)^(2.6n). - _Charles R Greathouse IV_, Dec 22 2011

%F min{k: k*A006882(n) in A000040}.

%e a(7) = 4 because 4*7!! - 1 = 4*105 - 1 = 419 is prime.

%p A202449 := proc(n)

%p     for k from 1 do

%p         if isprime(k*doublefactorial(n)-1) then

%p             return k;

%p         end if;

%p     end do:

%p end proc:

%p seq(A202449(n),n=1..80) ; # _R. J. Mathar_, Dec 22 2011

%t Table[k = 0; While[!PrimeQ[k*n!! -1], k++]; k, {n, 85}]

%o (PARI) a(n)=my(N=prod(k=1,n\2,2*k+n%2),k);while(!isprime(k++*N-1), ); k \\ _Charles R Greathouse IV_, Dec 22 2011

%K nonn

%O 1,1

%A _Michel Lagneau_, Dec 19 2011