A263347 Odd numbers n such that for every k >= 1, n*2^k + 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

37158601, 1017439067, 1242117623, 1554424697, 1905955429, 2727763433, 4512543497, 4798554619, 4954643117, 4988327659, 5367644183, 5660978867, 6107173883, 7173264623, 7425967459, 8365215091, 8776906457, 9013226179, 9095014883, 9787717801, 10466795551

Offset: 1

Author

Arkadiusz Wesolowski, Oct 15 2015

Keywords

• nonn

Comments

Cohen and Selfridge showed that this sequence contains infinitely many numbers that are both Sierpiński and Riesel.

What is the smallest term of this sequence that belongs to A076335? Is it the smallest Brier number?

This sequence contains only numbers of the form 30*k + 1, 30*k + 17, 30*k + 19, and 30*k + 23.

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..96
• Chris Caldwell, The Prime Glossary, Sierpinski number
• Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), pp. 79-81.
• Carlos Rivera, Problem 29 and Problem 58
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A076335, A263561.

Subsequence of A076336.

A263560 gives the primes.

Formula

a(n) = a(n-96) + 39832304070 for n > 96.