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%I #14 May 26 2024 14:41:57
%S 0,1,3,6,10,18,21,34,44,105,154,163,189,382,421,2473,2664,4590,9804,
%T 19950,29992,38457,40249,124656,185139,195032
%N Numbers k such that 56*10^k - 3 is prime.
%C For k > 0, numbers k such that the digits 55 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).
%C a(27) > 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 559w7</a>.
%e 3 is in this sequence because 56*10^3 - 3 = 55997 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 53;
%e a(2) = 1, 557;
%e a(3) = 3, 55997;
%e a(4) = 6, 55999997;
%e a(5) = 10, 559999999997; etc.
%t Select[Range[0, 100000], PrimeQ[56*10^# - 3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,3
%A _Robert Price_, Aug 27 2017
%E a(24)-a(26) from _Robert Price_, Mar 17 2020