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%I #13 May 18 2024 13:37:43
%S 0,2,5,9,24,50,63,98,117,164,932,1086,3465,5706,6311,6440,8985,10397,
%T 14157,23528,100611,144648,164984
%N Numbers k such that (76*10^k + 77)/9 is prime.
%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 4 followed by the digits 53 is prime (see Example section).
%C a(24) > 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 84w53</a>.
%e 2 is in this sequence because (76*10^2 + 77)/9 = 853 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 17;
%e a(2) = 2, 853;
%e a(3) = 5, 844453;
%e a(4) = 9, 8444444453;
%e a(5) = 24, 8444444444444444444444453; etc.
%t Select[Range[0, 100000], PrimeQ[(76*10^# + 77)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 05 2017
%E a(21)-a(23) from _Robert Price_, Sep 30 2019