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Numbers k such that (56*10^k + 403)/9 is prime.
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%I #13 May 19 2024 21:55:55

%S 1,7,8,11,35,37,49,127,149,188,1214,3020,5666,6254,7874,8281,11095,

%T 13831,20785,20854,31249,40031,40450,63100

%N Numbers k such that (56*10^k + 403)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k - 2 occurrences of the digit 2 followed by the digits 67 is prime (see Example section).

%C a(25) > 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 62w67</a>.

%e 1 is in this sequence because (56*10^1 + 403)/9 = 107 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 107;

%e a(2) = 7, 62222267;

%e a(3) = 8, 622222267;

%e a(4) = 11, 622222222267;

%e a(5) = 35, 622222222222222222222222222222222267; etc.

%t Select[Range[0, 100000], PrimeQ[(56 * 10^# + 403)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 31 2017