A046070 Second smallest m such that (2n-1)2^m-1 is prime, or -1 if no such value exists.

3, 1, 4, 5, 3, 26, 7, 2, 4, 3, 2, 6, 9, 2, 16, 5, 3, 6, 2553, 24, 10, 31, 2, 14, 5, 9, 6, 3, 2, 16, 5, 3, 6, 9, 4, 14, 11, 3, 4, 3, 5, 4, 11, 2, 8, 3, 4, 6, 9, 4, 18, 7, 3, 12, 149, 3, 14, 3, 2, 16, 3, 3, 4, 113, 3, 14, 11, 9, 18, 5, 2, 4, 13, 2, 16, 221, 4, 8, 5, 4, 6, 31, 3, 6, 5, 3, 4, 3

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

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.

Crossrefs

Cf. A046068, A046069.

Programs

Mathematica

max = 10000 (* this maximum value of m is sufficient up to n=168 *); a[n_] := Reap[ For[m = 0; 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]]; Table[a[n][[2]], {n, 1, 88}] (* Jean-François Alcover, Feb 28 2013 *)