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A275236 Numbers k such that (28*10^k - 97)/3 is prime.

%I A275236 #24 May 02 2024 04:26:13
%S A275236 1,5,8,20,27,56,74,81,107,217,294,326,525,645,667,764,863,1885,1961,
%T A275236 2913,3056,3192,3327,5480,8455,22797,50147,89141,96265
%N A275236 Numbers k such that (28*10^k - 97)/3 is prime.
%C A275236 For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 01 is prime (see Example section).
%C A275236 a(30) > 10^5.
%H A275236 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275236 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 93w01</a>.
%e A275236 5 is in this sequence because (28*10^5-97)/3 = 877 is prime.
%e A275236 Initial terms and associated primes:
%e A275236 a(1) = 1, 61;
%e A275236 a(2) = 5, 933301;
%e A275236 a(3) = 8, 933333301;
%e A275236 a(4) = 20, 933333333333333333301;
%e A275236 a(5) = 27, 9333333333333333333333333301, etc.
%t A275236 Select[Range[0, 100], PrimeQ[(28*10^#-97)/3 && # > 0] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)
%o A275236 (PARI) is(n)=ispseudoprime((28*10^n-97)/3) \\ _Charles R Greathouse IV_, Jul 21 2016
%o A275236 (Magma) [n: n in [1..500] | IsPrime((28*10^n-97) div 3)]; // _Vincenzo Librandi_, Jul 21 2016
%Y A275236 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275236 nonn,more
%O A275236 1,2
%A A275236 _Robert Price_, Jul 20 2016