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%I #26 Jul 14 2023 01:37:44
%S 1,3,4,9,10,12,13,16,20,37,57,66,106,116,127,355,396,547,2289,3777,
%T 4500,7821,15663,22746,25978,30434,39682,119716,133390,145093,200260
%N Numbers k such that (19*10^k + 101) / 3 is prime.
%C For k>1, numbers such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 67 is prime (see Example section).
%C a(32) > 3*10^5. - _Robert Price_, Jul 13 2023
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficulty.txt">Search for 63w67</a>.
%e 3 is in this sequence because (19*10^3 + 101) / 3 = 6367 is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 97;
%e a(2) = 3, 6367;
%e a(3) = 4, 63367;
%e a(4) = 9, 6333333367;
%e a(5) = 10, 63333333367, etc.
%t Select[Range[0, 100000], PrimeQ[(19*10^# + 101) / 3] &]
%o (Magma) [n: n in [0..400] |IsPrime((19*10^n + 101) div 3)]; // _Vincenzo Librandi_, Sep 13 2016
%o (PARI) is(n)=ispseudoprime((19*10^n + 101)/3) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Sep 12 2016
%E a(28)-a(30) from _Robert Price_, Sep 01 2019
%E a(31) from _Robert Price_, Jul 13 2023
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