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%I #19 May 25 2024 15:38:53
%S 2,5,7,8,11,13,25,26,61,82,131,289,377,547,845,929,1786,5887,6562,
%T 10546,28033,33493,150515,205183
%N Numbers k such that (43*10^k - 421)/9 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 31 is prime (see Example section).
%C a(25) > 3*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 47w31</a>.
%e 4 is in this sequence because (43*10^4 - 421)/9 = 477731 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 431;
%e a(2) = 5, 477731;
%e a(3) = 7, 47777731;
%e a(4) = 8, 477777731;
%e a(5) = 11, 477777777731; etc.
%t Select[Range[1, 100000], PrimeQ[(43*10^# - 421)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Apr 09 2017
%E a(23) from _Robert Price_, Jan 21 2019
%E a(24) from _Robert Price_, Oct 25 2023