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%I #13 May 05 2024 00:20:56
%S 1,4,7,8,18,19,73,143,192,408,533,792,3179,7709,9554,35598,41587,
%T 52919,56021,61604,78672,81624
%N Numbers k such that 15*10^k + 1 is prime.
%C For k > 1, numbers k such that the digits 15 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
%C a(23) > 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 150w1</a>.
%e 4 is in this sequence because 15*10^4 + 1 = 150001 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 151;
%e a(2) = 4, 150001;
%e a(3) = 7, 150000001;
%e a(4) = 8, 1500000001;
%e a(5) = 18, 15000000000000000001; etc.
%t Select[Range[0, 100000], PrimeQ[15*10^# + 1] &]
%o (PARI) isok(k) = isprime(15*10^k + 1); \\ _Michel Marcus_, Nov 20 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 19 2017