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

1,2

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

Table of n, a(n) for n=1..88.

Eric Weisstein's World of Mathematics, Riesel Number.

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

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 *)

Crossrefs

Cf. A046067, A046070.

Sequence in context: A293446 A360378 A256443 * A166281 A330954 A107468

Adjacent sequences: A046065 A046066 A046067 * A046069 A046070 A046071

Keyword

sign

Author

Eric W. Weisstein

Status

approved