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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}.

%I A263347 #32 Apr 03 2023 10:36:13
%S A263347 37158601,1017439067,1242117623,1554424697,1905955429,2727763433,
%T A263347 4512543497,4798554619,4954643117,4988327659,5367644183,5660978867,
%U A263347 6107173883,7173264623,7425967459,8365215091,8776906457,9013226179,9095014883,9787717801,10466795551
%N 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}.
%C A263347 Cohen and Selfridge showed that this sequence contains infinitely many numbers that are both Sierpiński and Riesel.
%C A263347 What is the smallest term of this sequence that belongs to A076335? Is it the smallest Brier number?
%C A263347 This sequence contains only numbers of the form 30*k + 1, 30*k + 17, 30*k + 19, and 30*k + 23.
%H A263347 Arkadiusz Wesolowski, <a href="/A263347/b263347.txt">Table of n, a(n) for n = 1..96</a>
%H A263347 Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/SierpinskiNumber.html">Sierpinski number</a>
%H A263347 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 A263347 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 A263347 <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 A263347 a(n) = a(n-96) + 39832304070 for n > 96.
%Y A263347 Cf. A076335, A263561.
%Y A263347 Subsequence of A076336.
%Y A263347 A263560 gives the primes.
%K A263347 nonn
%O A263347 1,1
%A A263347 _Arkadiusz Wesolowski_, Oct 15 2015