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%I #12 May 18 2024 11:32:28
%S 1,2,4,10,23,41,47,61,137,278,388,523,992,3716,4438,5185,7553,9970,
%T 17962,18568,36796,112919,114737,116842
%N Numbers k such that (85*10^k + 293)/9 is prime.
%C For k>1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 4 followed by the digits 77 is prime (see Example section).
%C a(25) > 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 94w77</a>.
%e 2 is in this sequence because (85*10^2 + 293)/9 = 977 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 127;
%e a(2) = 2, 977;
%e a(3) = 4, 94477;
%e a(4) = 10, 94444444477;
%e a(5) = 23, 944444444444444444444477; etc.
%t Select[Range[1, 100000], PrimeQ[(85*10^# + 293)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 06 2017
%E a(22)-a(24) from _Robert Price_, Dec 13 2019