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A046067 Smallest m such that (2n-1)2^m+1 is prime, or -1 if no such value exists. 15
0, 1, 1, 2, 1, 1, 2, 1, 3, 6, 1, 1, 2, 2, 1, 8, 1, 1, 2, 1, 1, 2, 2, 583, 2, 1, 1, 4, 2, 5, 4, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 4, 2, 1, 8, 2, 1, 2, 1, 3, 16, 1, 3, 6, 1, 1, 2, 3, 1, 8, 6, 1, 2, 3, 1, 4, 1, 3, 2, 1, 53, 6, 8, 3, 4, 1, 1, 8, 6, 3, 2, 1, 7, 2, 8, 1, 2, 2, 1, 4, 1, 3, 6, 1, 1, 2, 4, 15, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

The smallest known example is 78557. Therefore a(39279) = -1.

For the corresponding primes see A057025(n-1), n >= 1, where a 0 will show up if a(n) = -1. - Wolfdieter Lang, Feb 07 2013.

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n=1..5000 (with help from the Sierpiński problem website)

Ray Ballinger and Wilfrid Keller, Sierpiński Problem

John R. Cowles and Ruben Gamboa, Verifying Sierpiński and Riesel Numbers in ACL2, arXiv preprint arXiv:1110.4671, 2011

Seventeen or Bust, A Distributed Attack on the Sierpiński Problem

W. Sierpiński, Sur un problème concernant les nombres k*2^n+1.

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 = 1000 *); a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[(2n - 1)*2^m + 1], Return[m]]] /. Null -> -1; a[1] = 0; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 08 2012 *)

CROSSREFS

Cf. A046068.

Bisection of A040076. Cf. A033809.

Cf. A057192, A057025.

Sequence in context: A309035 A071628 A033809 * A305531 A132066 A102190

Adjacent sequences:  A046064 A046065 A046066 * A046068 A046069 A046070

KEYWORD

sign

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 13 16:08 EST 2019. Contains 329106 sequences. (Running on oeis4.)