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Numbers k such that 5*10^(2*k) + 5*10^k + 1 is prime.
1

%I #18 Sep 03 2024 16:33:41

%S 0,3,5,301,13817,15259

%N Numbers k such that 5*10^(2*k) + 5*10^k + 1 is prime.

%C 11 | 5*10^(4*m) + 5*10^(2*m) + 1. So a(n) is odd for n > 1.

%e 11 is prime ==> a(1) = 0.

%e 551 = 19 * 29.

%e 50501 = 11 * 4591.

%e 5005001 is prime ==> a(2) = 3.

%e 500050001 = 11 * 61 * 745231.

%e 50000500001 is prime ==> a(3) = 5.

%e 5000005000001 = 11 * 31 * 1801 * 8141461.

%o (PARI) for(k=0, 1e3, if(ispseudoprime(5*100^k+5*10^k+1), print1(k", ")))

%Y Cf. A309739.

%K nonn,base,more

%O 1,2

%A _Seiichi Manyama_, Aug 15 2019

%E a(5)-a(6) from _Michael S. Branicky_, Sep 03 2024