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%I #14 Sep 29 2023 19:12:59
%S 4,4,6,34,4,18,4,10,34,60,208,442,976,1548,1918,1726,3828,210,17940,
%T 34254,1852,19986,7728,22186,9966
%N Least k such that k*A000668(n)*A000668(n+2) + 1 is prime, where A000668(n) is the n-th Mersenne prime.
%C If they exist, a(26) > 31373, a(27) > 419, a(28) > 87.
%t Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[k*(2^MersennePrimeExponent[n]-1)*(2^(MersennePrimeExponent[n+2])-1)+1],Break[]];k++];k],k],{n,1,25}]
%Y Cf. A000668 (Mersenne primes), A098917, A365064, A365065.
%K nonn,more
%O 1,1
%A _J.W.L. (Jan) Eerland_, Aug 19 2023
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