%I #43 Sep 07 2024 08:00:23
%S 0,10,118,138,1143,16344,19324
%N Numbers k such that 36*10^(2*k) + 6*10^k + 1 is prime.
%C a(6) > 6000. - _Tyler NeSmith_, Dec 05 2021
%e 43 is prime ==> a(1) = 0.
%e 3661 = 7 * 523.
%e 360601 = 19 * 18979.
%e 36006001 = 67 * 537403.
%e 3600060001 = 457 * 7877593.
%e 360000600001 = 7 * 51428657143.
%e 36000006000001 = 379 * 94986823219.
%e 3600000060000001 = 7 * 43 * 64609 * 185115589.
%e 360000000600000001 = 19 * 18947368452631579.
%e 36000000006000000001 = 307 * 1249 * 1071121 * 87652267.
%e 3600000000060000000001 is prime ==> a(2) = 10.
%o (PARI) for(k=0, 1e3, if(ispseudoprime(36*100^k+6*10^k+1), print1(k", ")))
%Y Cf. A309738.
%K nonn,more,base
%O 1,2
%A _Seiichi Manyama_, Aug 15 2019
%E a(6) from _Michael S. Branicky_, Apr 24 2023
%E a(7) from _Michael S. Branicky_, Sep 07 2024