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A272537 Numbers k such that (28*10^k + 173)/3 is prime.

%I A272537 #20 Jul 02 2024 18:45:32
%S A272537 0,1,2,3,9,11,13,15,17,24,37,44,48,58,65,104,393,413,1265,2292,2620,
%T A272537 3037,3628,5159,5629,12809,18572,26875,29695,32267,34277,43621,138768,
%U A272537 220800
%N A272537 Numbers k such that (28*10^k + 173)/3 is prime.
%C A272537 For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 91 is prime (see Example section).
%C A272537 a(35) > 3*10^5.
%H A272537 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A272537 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 93w91</a>.
%e A272537 3 is in this sequence because (28*10^3 + 173)/3 = 9391 is prime.
%e A272537 Initial terms and associated primes:
%e A272537 a(1) = 0, 67;
%e A272537 a(2) = 1, 151;
%e A272537 a(3) = 2, 991;
%e A272537 a(4) = 3, 9391;
%e A272537 a(5) = 9, 9333333391, etc.
%t A272537 Select[Range[0, 100000], PrimeQ[(28*10^# + 173)/3] &]
%o A272537 (PARI) is(n)=ispseudoprime((28*10^n + 173)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A272537 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A272537 nonn,more
%O A272537 1,3
%A A272537 _Robert Price_, May 02 2016
%E A272537 a(33) from _Robert Price_, Dec 25 2019
%E A272537 a(34) from _Robert Price_, Jul 02 2024