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%I #14 May 03 2024 07:45:29
%S 1,2,7,10,16,22,32,85,106,310,374,410,421,502,850,938,1213,2362,4597,
%T 50578,59509,77572,136141,174790
%N Numbers k such that (47*10^k + 493)/9 is prime.
%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 2 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 52w77</a>.
%e 2 is in this sequence because (47*10^2 + 493)/9 = 577 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 107;
%e a(2) = 2, 577;
%e a(3) = 7, 52222277;
%e a(4) = 10, 52222222277;
%e a(5) = 16, 52222222222222277; etc.
%t Select[Range[0, 100000], PrimeQ[(47*10^# + 493)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 28 2017
%E a(23)-a(24) from _Robert Price_, Mar 23 2019