%I #10 Aug 12 2015 20:47:26
%S 2,1,1,2,1,3,1,2,4,6,4,2,1,8,4,3,1,3,1,27,13,6,25,12,38,21,10,15,7,3,
%T 1,9,4,5,2,23,11,5,2,24,23,11,5,2,13,6,19,9,4,18,10
%N Smallest strictly positive integer k such that (k+1)*2^n-1 is prime.
%C The associated prime number list is (k+1)*2^n-1 = 2, 3, 7, 23, 31, 127, 127, 383, 1279, 3583, 5119, 6143, 8191, 73727 for n=0,1,2,3,4,... - _R. J. Mathar_, Jan 22 2007
%F a(n)=A127587(n) if n is not in A000043. - _R. J. Mathar_, Jan 22 2007
%F a(n) << 19^n by Xylouris' improvement to Linnik's theorem. - _Charles R Greathouse IV_, Dec 10 2013
%p A127586 := proc(n) local k; k:=1 ; while true do if isprime( (k+1)*2^n-1) then RETURN(k) ; fi ; k := k+1 ; od ; end: for n from 0 to 100 do printf("%d, ",A127586(n)) ; od ; # _R. J. Mathar_, Jan 22 2007
%t a = {}; Do[k = 1; While[ ! PrimeQ[k 2^n + 2^n - 1], k++ ]; AppendTo[a, k], {n, 0, 50}]; a
%Y Cf. A007522, A127575, A127576, A127577, A127578, A127580, A127581, A087522, A127587.
%K nonn
%O 0,1
%A _Artur Jasinski_, Jan 19 2007