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Numbers k such that (22*10^k + 257)/9 is prime.
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%I #12 May 11 2024 19:12:26

%S 1,3,4,6,22,31,201,265,340,388,396,561,1224,2841,3234,3538,8473,12061,

%T 29347,62926,146029

%N Numbers k such that (22*10^k + 257)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 4 followed by the digits 73 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 24w73</a>.

%e 3 is in this sequence because (22*10^3 + 257)/9 = 2473 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 53;

%e a(2) = 3, 2473;

%e a(3) = 4, 24473;

%e a(4) = 6, 2444473;

%e a(5) = 22, 24444444444444444444473; etc.

%t Select[Range[0, 100000], PrimeQ[(22*10^# + 257)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 12 2017

%E a(21) from _Robert Price_, Jun 08 2018