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%I #7 Jul 17 2021 11:21:56
%S 1,1,2,6,40,17,4,6,47,48,334,99,585,19,350,1201,197,3577,2020,870,
%T 2322,4488,6150,12397,7817
%N Least number k such that 4*(k*(2^p-1))^2 + 1 is prime where 2^p-1 is a Mersenne prime (p in A000043).
%e a(1) = 1 since 3 = 2^A000043(1) - 1 and 4*(1*3)^2 + 1 = 37 is prime.
%t f[n_] := Module[{k = 1}, While[!PrimeQ[4*(k*n)^2 + 1], k++]; k]; f /@ (2^MersennePrimeExponent[Range[15]] - 1)(* _Amiram Eldar_, Jul 17 2021 *)
%Y Cf. A000043, A000668.
%K nonn,more
%O 1,3
%A _Pierre CAMI_, Nov 05 2007
%E Data corrected and a(23)-a(25) added by _Amiram Eldar_, Jul 17 2021
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