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A271506 Numbers k such that (7*10^k + 179)/3 is prime.

%I A271506 #20 Jun 06 2024 23:24:00
%S A271506 1,2,3,7,8,36,41,46,74,76,88,103,115,188,194,257,310,399,511,515,776,
%T A271506 1134,1404,6545,6569,17600,22209,24397,24842,46957,116684,118607,
%U A271506 131339,202267
%N A271506 Numbers k such that (7*10^k + 179)/3 is prime.
%C A271506 For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 93 is prime (see Example section).
%C A271506 a(35) > 3*10^5.
%H A271506 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A271506 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 23w93</a>.
%e A271506 3 is in this sequence because (7*10^3 + 179)/3 = 2393 is prime.
%e A271506 Initial terms and associated primes:
%e A271506 a(1) = 1, 83;
%e A271506 a(2) = 2, 293;
%e A271506 a(3) = 3, 2393;
%e A271506 a(4) = 7, 23333393;
%e A271506 a(5) = 8, 233333393. etc.
%t A271506 Select[Range[0, 100000], PrimeQ[(7*10^# + 179)/3] &]
%t A271506 Join[{1},Flatten[Position[Table[100*FromDigits[PadRight[{2},n,3]]+93,{n,47000}],_?PrimeQ]]+1] (* _Harvey P. Dale_, Dec 11 2018 *)
%o A271506 (PARI) is(n)=ispseudoprime((7*10^n+179)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A271506 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271506 nonn,more
%O A271506 1,2
%A A271506 _Robert Price_, Apr 08 2016
%E A271506 a(31)-a(33) from _Robert Price_, Sep 01 2018
%E A271506 a(34) from _Robert Price_, Jun 21 2023