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Least k such that k*2^m - 1 has a covering set with precisely n primes.
1

%I #11 Apr 20 2012 21:17:04

%S 509203,777149,7106977,60014203

%N Least k such that k*2^m - 1 has a covering set with precisely n primes.

%C A set of primes is a covering set for k*2^m - 1 if for every positive integer m there is some prime in the set which divides k*2^m - 1. Only minimal covering sets are considered here (those which would not remain covering sets with the removal of any element).

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Covering_set">Covering set</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riesel_number">Riesel number</a>

%e 509203 has the covering set {3, 5, 7, 13, 17, 241}.

%e 777149 has the covering set {3, 5, 7, 13, 19, 37, 73}.

%e 7106977 has the covering set {3, 5, 13, 17, 19, 109, 241, 433}.

%e 60014203 has the covering set {3, 5, 7, 11, 13, 31, 41, 61, 151}.

%Y Cf. A076337, A101036.

%K more,nonn

%O 6,1

%A _Arkadiusz Wesolowski_, Apr 19 2012