%I #15 Jun 02 2024 14:04:24
%S 1,3,4,9,10,11,14,25,38,74,110,133,145,469,1035,1808,3323,4534,4875,
%T 5306,16645,20591,25904,29365,81488,108184,132550
%N Numbers k such that (19*10^k + 191)/3 is prime.
%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).
%C a(28) > 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 63w97</a>.
%e 4 is in this sequence because (19*10^4 + 191) / 3 = 63397 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 127;
%e a(2) = 3, 6397;
%e a(3) = 4, 63397;
%e a(4) = 9, 6333333397;
%e a(5) = 10, 63333333397; etc.
%t Select[Range[0, 100000], PrimeQ[(19*10^# + 191) / 3] &]
%o (PARI) isok(n) = isprime((19*10^n + 191)/3); \\ _Michel Marcus_, Jan 07 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Jan 06 2017
%E a(26)-a(27) from _Robert Price_, May 09 2019