%I #17 Jun 10 2024 23:36:17

%S 0,1,2,6,20,23,86,146,167,340,472,500,898,907,936,1133,2069,3166,4207,

%T 5275,9700,20407,28009,32923,53264

%N Numbers k such that (22*10^k + 71)/3 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 57 is prime (see Example section).

%C a(26) > 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 73w57</a>.

%e 2 is in this sequence because (22*10^2 + 71)/3 = 757 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 31;

%e a(2) = 1, 97;

%e a(3) = 2, 757;

%e a(4) = 6, 7333357;

%e a(5) = 20, 733333333333333333357; etc.

%t Select[Range[0, 100000], PrimeQ[(22*10^# + 71)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, May 09 2017