%I #11 Jun 02 2024 09:29:20
%S 0,1,5,8,12,13,14,15,33,98,123,260,485,1340,1674,1775,5988,7039,9421,
%T 15149,21751,30882,36517,85839,121633,131180,140091,188823
%N Numbers k such that (16*10^k + 167)/3 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).
%C a(29) > 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 53w89</a>.
%e 5 is in this sequence because (16*10^5 + 167)/3 = 533389 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 61;
%e a(2) = 1, 109;
%e a(3) = 5, 533389;
%e a(4) = 8, 533333389;
%e a(5) = 12, 5333333333389; etc.
%t Select[Range[0, 100000], PrimeQ[(16*10^# + 167)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Oct 25 2017
%E a(25)-a(28) from _Robert Price_, Jun 18 2019