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a(n) is the smallest natural number m such that 10^10^k + m is prime for k = 0, 1, ...., n.
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%I #15 Mar 16 2014 10:59:51

%S 1,19,5641,1289743,2578966671

%N a(n) is the smallest natural number m such that 10^10^k + m is prime for k = 0, 1, ...., n.

%e 29 (=10^1+19) and 10000000019 (=10^10+19) are primes so a(1)=19.

%o (PARI) okm(m, n) = {for (k=0, n, if (!isprime(10^10^k + m), return (0)););return (1);}

%o a(n) = {m = 0; while (!okm(m, n), m++); m;} \\ _Michel Marcus_, Mar 16 2014

%Y Cf. A129613, A129614, A129615.

%K nonn,hard,more

%O 0,2

%A _Farideh Firoozbakht_, Mar 13 2014

%E a(4) from _Giovanni Resta_, Mar 14 2014