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%I #13 May 05 2024 00:21:29
%S 1,2,5,8,14,23,24,26,41,62,85,137,209,446,1424,1783,3301,5503,5928,
%T 9593,18671,40189,60655,113586,172692
%N Numbers k such that 5*10^k + 57 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 57 is prime (see Example section).
%C a(26) > 2*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 50w57</a>.
%e 2 is in this sequence because 5*10^2 + 57 = 557 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 107;
%e a(2) = 2, 557;
%e a(3) = 5, 500057;
%e a(4) = 8, 500000057;
%e a(5) = 14, 500000000000057; etc.
%t Select[Range[0, 100000], PrimeQ[5*10^# + 57] &]
%o (PARI) isok(k) = isprime(5*10^k + 57); \\ _Michel Marcus_, Nov 22 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard,changed
%O 1,2
%A _Robert Price_, Nov 21 2017
%E a(24)-a(25) from _Robert Price_, Dec 28 2018
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