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%I #30 Aug 08 2024 09:50:24
%S 1,2,6,7,8,315,667,5125,7301,10500,11096
%N Numbers k such that 2*10^(2k)-2*10^k+1 is prime.
%C Numbers of this form divide 4*10^(4k)+1.
%C a(8) > 5000. - _Jon E. Schoenfield_, Dec 16 2017
%C a(12) > 25000. - _Michael S. Branicky_, Aug 08 2024
%e 181, 19801, 1999998000001, 199999980000001, and 19999999800000001 are prime, while 1998001=277*7213, 199980001=13*41*457*821, and 19999800001=53*5953*63389.
%t ParallelMap[If[PrimeQ[2*10^(2 #) - 2*10^# + 1], #, Nothing] &, Range@ 4000] (* _Robert G. Wilson v_, Dec 13 2017 *)
%o (PARI) isok(k) = isprime(2*10^(2*k)-2*10^k+1); \\ _Michel Marcus_, Dec 13 2017
%Y See A296444 for 2*10^(2k)+2*10^k+1.
%K nonn,more
%O 1,2
%A _Patrick A. Thomas_, Dec 13 2017
%E a(6)-a(7) from _Michel Marcus_, Dec 13 2017
%E a(8)-a(11) from _Michael S. Branicky_, Mar 31 2023