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%I #12 Jun 08 2024 15:41:38
%S 1,4,10,12,16,28,42,108,127,664,744,781,3036,3184,4753,5695,7350,8592,
%T 8694,15939,21822,24466,61821,196281
%N Numbers k such that (47*10^k + 403)/9 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 2 followed by the digits 67 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 52w67</a>.
%e 4 is in this sequence because (47*10^4 + 403)/9 = 52267 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 97;
%e a(2) = 4, 52267;
%e a(3) = 10, 52222222267;
%e a(4) = 12, 5222222222267;
%e a(5) = 16, 52222222222222267; etc.
%t Select[Range[0, 100000], PrimeQ[(47*10^# + 403)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Apr 21 2017
%E a(24) from _Robert Price_, Mar 07 2019