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.
0, 0, 0, 0, 0, 241, 73, 241, 151, 241, 151, 151, 241, 257, 257, 257
Offset: 1
Examples
Examples of the covering sets:
- for n = 6, the set is {3, 5, 7, 13, 17, 241},
- for n = 7, the set is {3, 5, 7, 13, 19, 37, 73},
- for n = 8, the set is {3, 5, 7, 17, 19, 37, 73, 241},
- for n = 9, the set is {3, 5, 7, 11, 13, 31, 41, 61, 151},
- for n = 10, the set is {3, 5, 7, 11, 17, 31, 41, 61, 151, 241},
- for n = 11, the set is {3, 5, 7, 11, 19, 31, 37, 41, 61, 73, 151},
- for n = 12, the set is {3, 7, 11, 13, 19, 31, 37, 41, 61, 73, 109, 151},
- for n = 13, the set is {3, 7, 11, 17, 19, 31, 37, 41, 61, 73, 109, 151, 241},
- for n = 14, the set is {3, 7, 11, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 257},
- for n = 15, the set is {3, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257},
- for n = 16, the set is {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257}.
Extensions
Corrected by Arkadiusz Wesolowski, Aug 04 2023