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%I #33 Apr 18 2023 02:48:11
%S 0,2,3,6,10,276,746,1090,1485,6186,8571
%N Numbers k such that 2*10^(2k) + 2*10^k + 1 are prime.
%C Numbers of this form divide 4*10^(4k)+1.
%e 5, 20201, 2002001, 2000002000001, and 200000000020000000001 are prime, while 221=13*17, 200020001=569*351529, and 20000200001=17*29*1129*35933.
%t ParallelMap[ If[ PrimeQ[2*10^(2 #) + 2*10^# + 1], #, Nothing] &, Range@ 6500] (* _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 A296443 for 2*10^(2k)-2*10^k+1.
%Y Cf. A297422, A309739.
%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(10) from _Robert G. Wilson v_, Dec 13 2017
%E a(1) = 0 inserted by _Seiichi Manyama_, Aug 15 2019
%E a(11) from _Michael S. Branicky_, Apr 16 2023
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