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%I #18 Jun 07 2024 14:32:37
%S 2,3,5,7,8,11,14,18,25,39,81,91,347,391,438,464,539,818,1051,1125,
%T 1598,3384,11966,79867,147313
%N Numbers k such that (11*10^k - 107) / 3 is prime.
%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 31 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 36w31</a>.
%e 3 is in this sequence because (11*10^3 - 107) / 3 = 3631 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 331;
%e a(2) = 3, 3631;
%e a(3) = 5, 366631;
%e a(4) = 7, 36666631;
%e a(5) = 8, 366666631; etc.
%t Select[Range[0, 100000], PrimeQ[(11*10^# - 107) / 3] &]
%o (PARI) is(n)=ispseudoprime((11*10^n - 107)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Nov 23 2016
%E First comment and second link corrected by _Robert Price_, May 23 2018
%E a(25) from _Robert Price_, Sep 30 2018
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