%I #32 Apr 03 2023 10:36:13
%S 37158601,1017439067,1242117623,1554424697,1905955429,2727763433,
%T 4512543497,4798554619,4954643117,4988327659,5367644183,5660978867,
%U 6107173883,7173264623,7425967459,8365215091,8776906457,9013226179,9095014883,9787717801,10466795551
%N 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}.
%C Cohen and Selfridge showed that this sequence contains infinitely many numbers that are both SierpiĆski and Riesel.
%C What is the smallest term of this sequence that belongs to A076335? Is it the smallest Brier number?
%C This sequence contains only numbers of the form 30*k + 1, 30*k + 17, 30*k + 19, and 30*k + 23.
%H Arkadiusz Wesolowski, <a href="/A263347/b263347.txt">Table of n, a(n) for n = 1..96</a>
%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/SierpinskiNumber.html">Sierpinski number</a>
%H Fred Cohen and J. L. Selfridge, <a href="http://www.jstor.org/stable/2005463">Not every number is the sum or difference of two prime powers</a>, Math. Comput. 29 (1975), pp. 79-81.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_029.htm">Problem 29</a> and <a href="http://www.primepuzzles.net/problems/prob_058.htm">Problem 58</a>
%H <a href="/index/Rec#order_97">Index entries for linear recurrences with constant coefficients</a>, 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).
%F a(n) = a(n-96) + 39832304070 for n > 96.
%Y Cf. A076335, A263561.
%Y Subsequence of A076336.
%Y A263560 gives the primes.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Oct 15 2015