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Numbers k such that (22*10^k - 37)/3 is prime.
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%I #26 May 25 2024 14:17:19

%S 1,3,5,6,11,12,15,21,23,25,30,64,71,72,409,1491,1555,4469,5289,7002,

%T 16174,16485,68133,73853,134111

%N Numbers k such that (22*10^k - 37)/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 21 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 73w21</a>.

%e 3 is in this sequence because (22*10^3 - 37)/3 = 7321 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 61;

%e a(2) = 3, 7321;

%e a(3) = 5, 733321;

%e a(4) = 6, 7333321;

%e a(5) = 11, 733333333321; etc.

%t Select[Range[1, 100000], PrimeQ[(22*10^# - 37)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, May 09 2017

%E a(25) from _Robert Price_, Apr 15 2019