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%I #14 May 03 2024 18:44:13
%S 1,2,4,5,14,17,19,29,40,56,62,82,104,121,181,286,1307,2197,5764,37120,
%T 91715
%N Numbers k such that (28*10^k + 701)/9 is prime.
%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 1 followed by the digits 89 is prime (see Example section).
%C a(22) > 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 31w89</a>.
%e 2 is in this sequence because (28*10^2 + 701)/9 = 389 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 109;
%e a(2) = 2, 389;
%e a(3) = 4, 31189;
%e a(4) = 5, 311189;
%e a(5) = 14, 311111111111189; etc.
%t Select[Range[0, 100000], PrimeQ[(28*10^# + 701)/9] &]
%o (PARI) isok(k) = isprime((28*10^k + 701)/9); \\ _Michel Marcus_, Nov 22 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 21 2017
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