%I #13 May 27 2024 07:16:25
%S 1,3,4,18,28,40,45,49,78,165,312,469,855,899,1137,1314,1410,3832,
%T 10518,24163,28792,36947,56909,58103,59797,139782
%N Numbers k such that (13*10^k + 191)/3 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).
%C a(27) > 2*10^5.
%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/prime_difficulty.txt">Search for 43w97</a>.
%e 3 is in this sequence because (13*10^3 + 191)/3 = 4397 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 107;
%e a(2) = 3, 4397;
%e a(3) = 4, 43397;
%e a(4) = 18; 4333333333333333397;
%e a(5) = 28, 43333333333333333333333333397; etc.
%t Select[Range[0, 100000], PrimeQ[(13*10^# + 191)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Aug 14 2017
%E a(26) from _Robert Price_, Nov 28 2018