%I #12 Jun 08 2024 00:00:24
%S 0,1,3,7,9,15,17,27,37,55,58,155,228,480,720,1305,1573,2173,2547,2767,
%T 5448,5500,9468,14268,35207,58155,102612,114340,124420,169559
%N Numbers k such that (4*10^k + 83)/3 is prime.
%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).
%C a(31) > 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 13w61</a>.
%e 3 is in this sequence because (4*10^3 + 83) / 3 = 1361 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 29;
%e a(2) = 1, 41;
%e a(3) = 3, 1361;
%e a(4) = 7, 13333361;
%e a(5) = 9, 1333333361; etc.
%t Select[Range[0, 100000], PrimeQ[(4*10^# + 83) / 3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Jan 09 2017
%E a(27)-a(30) from _Robert Price_, Feb 02 2018