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A275020 Numbers k such that (5*10^k + 91) / 3 is prime.

%I A275020 #22 May 25 2024 17:37:41
%S A275020 1,2,3,10,19,35,43,80,107,143,199,218,255,304,353,560,904,996,1051,
%T A275020 6141,8075,9913,11151,28469,75244,108960,122592,178206,187471,257431
%N A275020 Numbers k such that (5*10^k + 91) / 3 is prime.
%C A275020 For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).
%C A275020 a(31) > 3*10^5.
%H A275020 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275020 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 16w97</a>.
%e A275020 3 is in this sequence because (5*10^3 + 91) / 3 = 1697 is prime.
%e A275020 Initial terms and associated primes:
%e A275020 a(1) = 1, 47;
%e A275020 a(2) = 2, 197;
%e A275020 a(3) = 3, 1697;
%e A275020 a(4) = 10, 16666666697;
%e A275020 a(5) = 19, 16666666666666666697, etc.
%t A275020 Select[Range[0, 100000], PrimeQ[(5*10^# + 91) / 3] &]
%o A275020 (PARI) is(n)=ispseudoprime((5*10^n + 91)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A275020 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275020 nonn,more
%O A275020 1,2
%A A275020 _Robert Price_, Nov 12 2016
%E A275020 a(26)-a(29) from _Robert Price_, Apr 28 2018
%E A275020 a(30) from _Robert Price_, Oct 25 2023