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Numbers k such that (25*10^k + 161)/3 is prime.
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%I #11 Jun 10 2024 23:37:12

%S 1,2,3,6,12,14,29,31,35,58,77,79,108,122,154,895,1045,1763,3243,3605,

%T 9446,16119,19238,28562,87726,89413,107804,136303

%N Numbers k such that (25*10^k + 161)/3 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 87 is prime (see Example section).

%C a(29) > 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 83w87</a>.

%e 3 is in this sequence because (25*10^3 + 161) / 3 = 8387 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 137;

%e a(2) = 2, 887;

%e a(3) = 3, 8387;

%e a(4) = 6, 8333387;

%e a(5) = 12, 8333333333387; etc.

%t Select[Range[0, 100000], PrimeQ[(25*10^# + 161) / 3] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 14 2017

%E a(27)-a(28) from _Robert Price_, Sep 30 2019