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%I #17 Jun 10 2024 23:36:17
%S 0,1,2,6,20,23,86,146,167,340,472,500,898,907,936,1133,2069,3166,4207,
%T 5275,9700,20407,28009,32923,53264
%N Numbers k such that (22*10^k + 71)/3 is prime.
%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 57 is prime (see Example section).
%C a(26) > 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 73w57</a>.
%e 2 is in this sequence because (22*10^2 + 71)/3 = 757 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 31;
%e a(2) = 1, 97;
%e a(3) = 2, 757;
%e a(4) = 6, 7333357;
%e a(5) = 20, 733333333333333333357; etc.
%t Select[Range[0, 100000], PrimeQ[(22*10^# + 71)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, May 09 2017