A046068 Second smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists.

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, 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, 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

Offset: 1

Author

Eric W. Weisstein

Keywords

• sign

Comments

There exist odd integers 2k-1 such that (2k-1)2^n+1 is always composite.

References

• Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 357-359, 1996.

Links

• Eric Weisstein's World of Mathematics, Riesel Number.
• Eric Weisstein's World of Mathematics, Sierpiński Number of the Second Kind

Crossrefs

Cf. A046067, A046070.

Programs

Mathematica

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 *)