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Numbers k such that (10^k + 77)/3 is prime.
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%I #43 May 25 2024 19:08:21

%S 1,2,3,4,5,8,16,20,56,58,75,109,124,217,221,368,439,595,1309,6986,

%T 11600,20855,29327,34305,42145,44056,52667,75707,79067,81848,119836,

%U 164284,176584

%N Numbers k such that (10^k + 77)/3 is prime.

%C For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 59 is prime (see Example section).

%C a(34) > 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 3w59</a>.

%e 3 is in this sequence because (10^3 + 77)/3 = 359 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 29;

%e a(2) = 2, 59;

%e a(3) = 3, 359;

%e a(4) = 4, 3359;

%e a(5) = 5, 33359; etc.

%t Select[Range[0, 100000], PrimeQ[(10^# + 77)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 21 2017

%E a(31)-a(33) from _Robert Price_, Jan 18 2018