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A273042 Numbers k such that (28*10^k + 191)/3 is prime.

%I A273042 #20 May 26 2024 15:03:44
%S A273042 0,1,2,3,5,6,9,10,33,49,92,109,548,757,814,1289,1460,1644,2782,6355,
%T A273042 8028,9276,9366,9765,12002,12089,14491,16180,29102,30989,151682,
%U A273042 183403,190105,253210
%N A273042 Numbers k such that (28*10^k + 191)/3 is prime.
%C A273042 For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).
%C A273042 a(35) > 3*10^5.
%H A273042 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273042 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 93w97</a>.
%e A273042 3 is in this sequence because (28*10^3 + 191)/3 = 9397 is prime.
%e A273042 Initial terms and associated primes:
%e A273042 a(1) = 0, 73;
%e A273042 a(2) = 1, 157:
%e A273042 a(3) = 2, 997;
%e A273042 a(4) = 3, 9397;
%e A273042 a(5) = 5, 933397, etc.
%t A273042 Select[Range[0, 100000], PrimeQ[(28*10^# + 191)/3] &]
%o A273042 (PARI) is(n)=ispseudoprime((28*10^n + 191)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A273042 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273042 nonn,more
%O A273042 1,3
%A A273042 _Robert Price_, May 13 2016
%E A273042 a(31)-a(33) from _Robert Price_, Feb 27 2020
%E A273042 a(34) from _Robert Price_, Jul 12 2023