%I #17 May 26 2024 22:59:50
%S 1,3,6,16,30,33,36,37,85,288,561,805,850,1057,1192,1312,2571,4579,
%T 5223,5940,10191,18756,24564,29595,43891,65905,89118,97963,112003,
%U 139945,174101,195221
%N Numbers k such that 5*10^k + 81 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 81 is prime (see Example section).
%C a(33) > 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 50w81</a>.
%e 3 is in this sequence because 5*10^3 + 81 = 5081 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 131;
%e a(2) = 3, 5081;
%e a(3) = 6, 5000081;
%e a(4) = 16, 50000000000000081;
%e a(5) = 30, 5000000000000000000000000000081; etc.
%t Select[Range[0, 100000], PrimeQ[5*10^# + 81] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Aug 27 2017
%E a(29)-a(32) from _Robert Price_, Mar 04 2019
%E Terms reordered into ascending order by _Robert Price_, Apr 03 2022