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%I #12 May 25 2024 19:36:21
%S 1,4,7,13,17,31,47,64,226,251,268,310,352,394,478,599,1529,1679,11590,
%T 12922,13151,18808,47188,52450,83038,93217,128086,154853,175774
%N Numbers k such that (86*10^k - 221)/9 is prime.
%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 5 followed by the digits 31 is prime (see Example section).
%C a(39) > 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 95w31</a>.
%e 4 is in this sequence because (86*10^4 - 221)/9 = 95531 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 71;
%e a(2) = 4, 95531;
%e a(3) = 7, 95555531;
%e a(4) = 13, 95555555555531;
%e a(5) = 17, 955555555555555531; etc.
%t Select[Range[1, 100000], PrimeQ[(86*10^# - 221)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Jun 17 2017
%E a(27)-a(29) from _Robert Price_, Aug 31 2019