%I #14 Mar 06 2015 22:50:46
%S 1,2,3,4,2,3,8,2,15,10,4,9,4,4,3,60,6,3,4,2,11,6,9,1483,6,3,5,8,3,11,
%T 12,4,3,6,2,5,6,3,7,10,4,5,6,6,7,168,4,3,4,2,9,18,2,7,14,4,5,12,4,3,
%U 12,8,5,12,5,3,6,2,27,14,3,77,16,11,7,20,2,7,12,7,5,4,2,103,14,9,13,4
%N Second smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists.
%C There exist odd integers 2k-1 such that (2k-1)2^n+1 is always composite.
%D Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RieselNumber.html">Riesel Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiNumberoftheSecondKind.html">Sierpiński Number of the Second Kind</a>
%t max = 10000 (* this maximum value of m is sufficient up to n=191 *); a[n_] := Reap[ For[m = 1; cnt = 0, m <= max && cnt < 2, m++, If[m == max, Sow[-1], If[PrimeQ[(2*n - 1)*2^m + 1], cnt++; Sow[m]]]]][[2, 1]]; a[1] = {0, 1}; Table[a[n][[2]], {n, 1, 88}] (* _Jean-François Alcover_, Feb 27 2013 *)
%Y Cf. A046067, A046070.
%K sign
%O 1,2
%A _Eric W. Weisstein_