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%I #17 Apr 09 2023 02:05:01
%S 1,2,3,8,14,35,75,83,89,90,215,342,753,1452,4578,10337,25580,26381
%N Numbers k such that (2^k - k + 1)*2^k - 1 is prime.
%e 3 is in the sequence because (2^3 - 3 + 1)*2^3 - 1 = 47 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(1500) # _Michael S. Branicky_, Jan 11 2022
%Y Cf. A201356, A201357, A201358, A201359, A201360, A201362, A201363.
%K nonn,hard,more
%O 1,2
%A _Michel Lagneau_, Nov 30 2011
%E a(16) from _Michael S. Branicky_, Jan 11 2022
%E a(17)-a(18) from _Michael S. Branicky_, Apr 07 2023
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