cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A306151 Let k be a Sierpiński or Riesel number, and let p be the largest number in a set of n primes which cover every number of the form k*2^m + 1 (or of the form k*2^m - 1) with m >= 1. a(n) = 0 if no covering set with n primes exists, otherwise a(n) = p if and only if there exists no number k that has a covering set with precisely n primes and with largest prime < p.

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%I A306151 #15 Sep 06 2023 21:32:40
%S A306151 0,0,0,0,0,241,73,241,151,241,151,151,241,257,257,257
%N A306151 Let k be a Sierpiński or Riesel number, and let p be the largest number in a set of n primes which cover every number of the form k*2^m + 1 (or of the form k*2^m - 1) with m >= 1. a(n) = 0 if no covering set with n primes exists, otherwise a(n) = p if and only if there exists no number k that has a covering set with precisely n primes and with largest prime < p.
%e A306151 Examples of the covering sets:
%e A306151 - for n = 6, the set is {3, 5, 7, 13, 17, 241},
%e A306151 - for n = 7, the set is {3, 5, 7, 13, 19, 37, 73},
%e A306151 - for n = 8, the set is {3, 5, 7, 17, 19, 37, 73, 241},
%e A306151 - for n = 9, the set is {3, 5, 7, 11, 13, 31, 41, 61, 151},
%e A306151 - for n = 10, the set is {3, 5, 7, 11, 17, 31, 41, 61, 151, 241},
%e A306151 - for n = 11, the set is {3, 5, 7, 11, 19, 31, 37, 41, 61, 73, 151},
%e A306151 - for n = 12, the set is {3, 7, 11, 13, 19, 31, 37, 41, 61, 73, 109, 151},
%e A306151 - for n = 13, the set is {3, 7, 11, 17, 19, 31, 37, 41, 61, 73, 109, 151, 241},
%e A306151 - for n = 14, the set is {3, 7, 11, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 257},
%e A306151 - for n = 15, the set is {3, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257},
%e A306151 - for n = 16, the set is {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257}.
%Y A306151 Cf. A076336, A101036, A206001, A206430, A305473.
%K A306151 nonn,more
%O A306151 1,6
%A A306151 _Arkadiusz Wesolowski_, Jun 23 2018
%E A306151 Corrected by _Arkadiusz Wesolowski_, Aug 04 2023