A132192 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).
1, 1, 2, 6, 40, 17, 4, 6, 47, 48, 334, 99, 585, 19, 350, 1201, 197, 3577, 2020, 870, 2322, 4488, 6150, 12397, 7817
Offset: 1
Examples
a(1) = 1 since 3 = 2^A000043(1) - 1 and 4*(1*3)^2 + 1 = 37 is prime.
Programs
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Mathematica
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 *)
Extensions
Data corrected and a(23)-a(25) added by Amiram Eldar, Jul 17 2021