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Numbers k such that 4*10^(2k) + 2*(10^k) + 1 is prime.
2

%I #23 Apr 12 2018 02:52:26

%S 0,1,3,5,10,196,251,310,415,1107,2422

%N Numbers k such that 4*10^(2k) + 2*(10^k) + 1 is prime.

%C Numbers of this form divide 8*(10^3k)-1.

%C a(12) > 50000. - _Robert Price_, Apr 11 2018

%e 7, 421, 4002001, and 40000200001 are prime, while 40201=7*5743, 400020001=31*12903871, etc.

%p select(k->isprime(4*10^(2*k)+2*(10^k)+1),[$0..1000]); # _Muniru A Asiru_, Apr 11 2018

%t Select[Range[1500], PrimeQ[4 (10^(2 #)) + 2 (10^#) + 1] &] (* _Michael De Vlieger_, Dec 30 2017 *)

%o (PARI) isok(k) = isprime(4*10^(2*k)+2*(10^k)+1); \\ _Michel Marcus_, Dec 30 2017

%K nonn,more

%O 1,3

%A _Patrick A. Thomas_, Dec 30 2017

%E a(6)-a(10) from _Michael De Vlieger_, Dec 30 2017

%E a(11) from _Jon E. Schoenfield_, Jan 01 2018