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%I #12 May 26 2024 22:59:57
%S 1,2,4,5,8,29,43,62,85,107,172,557,1043,2395,4498,5818,7772,9125,
%T 12616,17252,23000,64904,71077,113162
%N Numbers k such that (46*10^k + 521)/9 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 1 followed by the digits 69 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 51w69</a>.
%e 4 is in this sequence because (46*10^4 + 521)/9 = 51169 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 109;
%e a(2) = 2, 569;
%e a(3) = 4, 51169;
%e a(4) = 5, 511169;
%e a(5) = 8, 511111169; etc.
%t Select[Range[0, 100000], PrimeQ[(46*10^# + 521)/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_, Feb 23 2019