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%I #18 Apr 12 2018 03:10:55
%S 1,2,3,15,175,449,16563
%N Numbers k such that (10^(2k) + 2*(10^k) + 4)/4 is prime.
%C Numbers of this form divide 10^(3k)-8.
%C a(7) > 3000. - _Jon E. Schoenfield_, Jan 02 2018
%C a(8) > 50000. - _Robert Price_, Apr 11 2018
%e 31, 2551, 250501, and 250000000000000500000000000001 are prime, while 25005001=7*79*103*439, 2500050001=19*2269*57991, etc.
%p select(k->isprime((10^(2*k)+2*(10^k)+4)/4),[$1..1000]); # _Muniru A Asiru_, Apr 11 2018
%t Select[Range[10^3], PrimeQ[(10^(2 #) + 2 (10^#) + 4)/4] &] (* _Michael De Vlieger_, Dec 30 2017 *)
%o (PARI) isok(k) = isprime((10^(2*k)+2*(10^k)+4)/4); \\ _Michel Marcus_, Dec 30 2017
%K nonn,more
%O 1,2
%A _Patrick A. Thomas_, Dec 30 2017
%E a(5)-a(6) from _Michel Marcus_, Dec 30 2017
%E a(7) from _Robert Price_, Apr 11 2018