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A271645 Numbers k such that (23*10^k + 91)/3 is prime.

%I A271645 #18 May 25 2024 15:38:30
%S A271645 1,2,4,15,16,19,20,26,38,47,52,75,122,191,246,257,294,305,374,592,682,
%T A271645 729,1092,2053,2997,4065,13936,17214,19059,37433,142105,214633,242909
%N A271645 Numbers k such that (23*10^k + 91)/3 is prime.
%C A271645 For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).
%C A271645 a(34) > 3*10^5.
%H A271645 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A271645 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 76w97</a>.
%e A271645 4 is in this sequence because (23*10^4 + 91)/3 = 76697 is prime.
%e A271645 Initial terms and associated primes:
%e A271645 a(1) = 1, 107;
%e A271645 a(2) = 2, 797;
%e A271645 a(3) = 4, 76697;
%e A271645 a(4) = 15, 7666666666666697;
%e A271645 a(5) = 16, 76666666666666697, etc.
%t A271645 Select[Range[0, 100000], PrimeQ[(23*10^# + 91)/3] &]
%o A271645 (PARI) is(n)=ispseudoprime((23*10^n + 91)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A271645 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271645 nonn,more
%O A271645 1,2
%A A271645 _Robert Price_, Apr 11 2016
%E A271645 a(31) from _Robert Price_, Aug 11 2019
%E A271645 a(32)-a(33) from _Robert Price_, May 31 2023