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

1,1

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).

Formula

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

Crossrefs

Cf. A076335, A263561.

Subsequence of A076336.

A263560 gives the primes.

Sequence in context: A028965 A273508 A340713 * A263560 A215130 A286037

Adjacent sequences: A263344 A263345 A263346 * A263348 A263349 A263350

Keyword

nonn

Author

Arkadiusz Wesolowski, Oct 15 2015

Status

approved