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%I #18 May 19 2024 21:55:37
%S 1,2,4,7,16,33,35,51,371,1539,1564,2897,3431,4448,6593,7066,7345,
%T 11770,20026,22114,23945,46946,60772
%N Numbers k such that 55*10^k + 7 is prime.
%C For k > 0, numbers k such that the digits 55 followed by k-1 occurrences of the digit 0 followed by the digit 7 is prime (see Example section).
%C a(24) > 3*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 550w7</a>.
%e 2 is in this sequence because 55*10^2 + 7 = 5507 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 557;
%e a(2) = 2, 5507;
%e a(3) = 4, 550007;
%e a(4) = 7, 550000007;
%e a(5) = 16, 550000000000000007; etc.
%t Select[Range[0, 100000], PrimeQ[55*10^# + 7] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Oct 29 2017