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Numbers k such that 9*10^(2*k) + 3*10^k + 1 is prime.
1

%I #41 Sep 05 2024 10:16:22

%S 0,5,14,77,104,2603,2657,24029

%N Numbers k such that 9*10^(2*k) + 3*10^k + 1 is prime.

%e 13 is prime ==> a(1) = 0.

%e 931 = 7^2 * 19.

%e 90301 = 73 * 1237.

%e 9003001 = 7 * 757 * 1699.

%e 900030001 = 13 * 4969 * 13933.

%e 90000300001 is prime ==> a(2) = 5.

%o (PARI) for(k=0, 1e3, if(ispseudoprime(9*100^k+3*10^k+1), print1(k", ")))

%Y Cf. A309738, A309743.

%K nonn,base,more

%O 1,2

%A _Seiichi Manyama_, Aug 15 2019

%E a(8) from _Michael S. Branicky_, Sep 05 2024