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%I #23 Aug 16 2024 10:10:42
%S 1,2,3,4,7,10,56,154,170,14728
%N Numbers k such that 10^(2k)/2 + 10^k + 1 are prime.
%C Numbers of this form divide 10^(4k)+4.
%C a(10) > 5000. - _Jon E. Schoenfield_, Dec 16 2017
%e 61, 5101, 501001, 50010001, and 50000000010000000001 are prime, while 5000100001=13*1597*240841, 500001000001=2357*212134493, etc.
%t ParallelMap[If[PrimeQ[10^(2 #)/2 + 10^# + 1], #, Nothing] &, Range@ 4000] (* _Robert G. Wilson v_, Dec 13 2017 *)
%o (PARI) isok(k) = isprime(10^(2*k)/2+10^k+1); \\ _Michel Marcus_, Dec 13 2017
%Y See A296445 for 10^(2k)/2 - 10^k + 1.
%K nonn,more
%O 1,2
%A _Patrick A. Thomas_, Dec 13 2017
%E a(8)-a(9) from _Michel Marcus_, Dec 13 2017
%E a(10) from _Michael S. Branicky_, Aug 16 2024