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%I #13 Jul 12 2023 13:00:29
%S 1,2,3,4,5,7,9,15,27,29,39,62,77,106,114,357,555,962,1013,2372,8235,
%T 16047,82323,294308
%N Numbers k such that (11*10^k + 91)/3 is prime.
%C For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).
%C a(25) > 3*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/primedifficulty.txt">Search for 36w97.</a>
%e 3 is in this sequence because (11*10^3 + 91)/3 = 3697 is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 67;
%e a(2) = 2, 397;
%e a(3) = 3, 3697;
%e a(4) = 4, 36697;
%e a(5) = 5, 366697; etc.
%t Select[Range[0, 100000], PrimeQ[(11*10^# + 91)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Feb 24 2017
%E a(24) from _Robert Price_, Jul 12 2023
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