A185372 - OEIS

%I #14 Mar 31 2012 10:24:05

%S 2,4,10,10,40,40,100,32296,65836,214510186,413879926,1772668756

%N Least positive integer which, when added to each of the first n Mersenne primes, yields all primes.

%C J. L. Selfridge proved that a(8) > 100.

%t lst = {}; p = 18; Do[p = Prime[n]; If[PrimeQ[2^p - 1], AppendTo[lst, p]], {n, p}]; Table[k = 1; While[i = 1; While[i <= n && PrimeQ[2^lst[[i]] + k], i++]; i <= n, k++]; k + 1, {n, Count[lst, _Integer]}]

%Y Cf. A000043.

%K hard,more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Jan 26 2012