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%I #13 May 11 2024 19:12:47
%S 7,13,25,40,58,133,229,232,310,358,778,977,1057,1271,4417,4757,5242,
%T 6413,11539,60583,149737
%N Numbers k such that (865*10^k - 1)/9 is prime.
%C For k > 1, numbers k such that the digits 96 followed by k occurrences of the digit 1 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 961w</a>.
%e 7 is in this sequence because (865*10^7 - 1)/9 = 961111111 is prime.
%e Initial terms and associated primes:
%e a(1) = 7, 961111111;
%e a(2) = 12, 961111111111111;
%e a(3) = 23, 961111111111111111111111111;
%e a(4) = 40, 961111111111111111111111111111111111111111; etc.
%t Select[Range[0, 100000], PrimeQ[(865*10^# - 1)/9] &]
%o (PARI) isok(k) = isprime((865*10^k - 1)/9); \\ _Michel Marcus_, Nov 12 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Nov 11 2017
%E a(21) from _Robert Price_, Apr 18 2020