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%I #13 May 03 2024 18:44:05
%S 1,3,5,6,21,39,114,239,246,348,906,1115,2801,2958,2982,4275,6581,8736,
%T 27051,115523,124335
%N Numbers k such that (41*10^k - 383)/9 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 13 is prime (see Example section).
%C a(22) > 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 45w13</a>.
%e 3 is in this sequence because (41*10^3 - 383)/9 = 4513 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 3;
%e a(2) = 3, 4513;
%e a(3) = 5, 455513;
%e a(4) = 6, 4555513;
%e a(5) = 21, 4555555555555555555513; etc.
%t Select[Range[1, 100000], PrimeQ[(41*10^# - 383)/9] &]
%o (PARI) isok(k) = isprime((41*10^k - 383)/9); \\ _Michel Marcus_, Nov 22 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 21 2017
%E a(20)-a(21) from _Robert Price_, Nov 16 2018
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