%I #12 Jun 02 2024 20:58:59
%S 1,3,4,7,10,24,37,46,63,64,91,114,367,453,1156,1347,1524,7153,10893,
%T 13548,15153,43093,61167,184993
%N Numbers k such that (49*10^k - 67)/9 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 37 is prime (see Example section).
%C a(25) > 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 54w37</a>.
%e 4 is in this sequence because (49*10^4 - 67)/9 = 54437 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 3, 5437;
%e a(3) = 4, 54437;
%e a(4) = 7, 54444437;
%e a(5) = 10, 54444444437; etc.
%t Select[Range[1, 100000], PrimeQ[(49*10^# - 67)/9] &]
%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(24) from _Robert Price_, Mar 15 2019