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%I #12 Jun 09 2024 18:05:13
%S 1,2,4,8,26,28,43,70,92,128,331,364,478,532,689,778,895,1210,5081,
%T 7855,17852,20864,42598,56858,120703,173854
%N Numbers k such that (71*10^k - 287)/9 is prime.
%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 8 followed by the digits 57 is prime (see Example section).
%C a(27) > 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 78w57</a>.
%e 4 is in this sequence because (71*10^4 - 287)/9 = 78857 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 47;
%e a(2) = 2, 757;
%e a(3) = 4, 78857;
%e a(4) = 8, 788888857;
%e a(5) = 26, 788888888888888888888888857; etc.
%t Select[Range[1, 100000], PrimeQ[(71*10^# - 287)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, May 16 2017
%E a(25)-a(26) from _Robert Price_, Sep 06 2019