A263500 Smallest positive b such that for all k >= 1 the numbers n*b^k + 1 are composite and gcd(n+1, b-1) = 1, or 0 if n > 1 is of the form 2^m - 1.

0, 14, 140324348, 34, 0, 8, 177744, 32, 14

Offset: 3

Author

Arkadiusz Wesolowski, Oct 19 2015

Keywords

• nonn
• more
• hard

Comments

a(2) = 131072, or it is a Sierpiński number multiplied by a power of 2.

Because a(1) = 8 but a(2) is unknown, we do not include it here; we set the offset to 3.

a(2) <= 201446503145165177.

Links

• Dan Krywaruczenko, A Reverse Sierpiński Number Problem, Rose-Hulman Undergraduate Mathematics Journal: Vol. 9: Iss. 2, Article 4, 2009.

Crossrefs

Cf. A123159.