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%I #26 May 02 2024 22:55:03
%S 1,2,4,7,10,13,15,20,22,33,34,108,117,130,193,273,280,654,775,1144,
%T 4014,4015,7701,10356,11478,12427,15075,44107,102597,118635
%N Numbers k such that (17*10^k + 13)/3 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 71 is prime (see Example section).
%C a(31) > 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 56w71</a>.
%e 4 is in this sequence because (17*10^4 + 13)/3 = 56671 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 61;
%e a(2) = 2, 571:
%e a(3) = 4, 56671;
%e a(4) = 7, 56666671;
%e a(5) = 10, 56666666671, etc.
%t Select[Range[0, 100000], PrimeQ[(17*10^# + 13)/3] &]
%o (PARI) is(n)=ispseudoprime((17*10^n + 13)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,changed
%O 1,2
%A _Robert Price_, May 19 2016
%E a(29)-a(30) from _Robert Price_, Jan 22 2019
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