%I #15 Apr 11 2023 07:54:21
%S 1,5,49,269,2387,2945,5897,11929,30433
%N Numbers k such that (2^k + k - 1)*2^k + 1 is prime.
%e 5 is in the sequence because (2^5 + 5 - 1)*2^5 + 1 = 1153 is prime.
%t lst={};Do[If[PrimeQ[(2^n + n-1)*2^n+1],AppendTo[lst,n]],{n,10000}];lst
%o (PARI) is(n)=ispseudoprime((2^n+n-1)<<n+1) \\ _Charles R Greathouse IV_, Feb 17 2017
%o (Python)
%o from sympy import isprime
%o def afind(limit, startk=1):
%o pow2 = 2**startk
%o for k in range(startk, limit+1):
%o if isprime((pow2 + k - 1)*pow2 + 1):
%o print(k, end=", ")
%o pow2 *= 2
%o afind(3000) # _Michael S. Branicky_, Jan 11 2022
%Y Cf. A201356, A201357, A201359, A201360, A201361, A201362, A201363.
%K nonn,hard,more
%O 1,2
%A _Michel Lagneau_, Nov 30 2011
%E a(8) from _Michael S. Branicky_, Jan 11 2022
%E a(9) from _Michael S. Branicky_, Apr 09 2023