%I
%S 1,2,3,10,19,35,43,80,107,143,199,218,255,304,353,560,904,996,1051,
%T 6141,8075,9913,11151,28469,75244,108960,122592,178206,187471
%N Numbers k such that (5*10^k + 91) / 3 is prime.
%C For k>1, numbers such that the digit 1 followed by k2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).
%C a(30) > 2*10^5.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of nearrepdigitrelated numbers</a>.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/primedifficulty.txt">Search for 16w97.</a>
%e 3 is in this sequence because (5*10^3 + 91) / 3 = 1697 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 2, 197;
%e a(3) = 3, 1697;
%e a(4) = 10, 16666666697;
%e a(5) = 19, 16666666666666666697, etc.
%t Select[Range[0, 100000], PrimeQ[(5*10^# + 91) / 3] &]
%o (PARI) is(n)=ispseudoprime((5*10^n + 91)/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_, Nov 12 2016
%E a(26)a(29) from _Robert Price_, Apr 28 2018
