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Numbers k such that (59*10^k - 77)/9 is prime.
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%I #20 May 18 2024 13:38:07

%S 2,3,5,6,9,14,21,29,30,32,39,59,69,113,410,13484,15525,16796,22064,

%T 37694,38103,73217

%N Numbers k such that (59*10^k - 77)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).

%C a(23) > 2*10^5.

%C All terms == 0 or 2 (mod 3). - _Robert Israel_, May 30 2019

%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 65w47</a>.

%e 2 is in this sequence because (59*10^2 - 77)/9 = 647 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 647;

%e a(2) = 3, 6547;

%e a(3) = 5, 655547;

%e a(4) = 6, 6555547;

%e a(5) = 9, 6555555547; etc.

%t Select[Range[1, 100000], PrimeQ[(59*10^# - 77)/9] &]

%o (PARI) is(n) = ispseudoprime((59*10^n - 77)/9) \\ _Felix Fröhlich_, May 30 2019

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 05 2017