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Numbers k such that (316*10^k - 1)/9 is prime.
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%I #11 Jun 08 2024 15:47:53

%S 2,3,8,9,11,14,17,23,29,38,50,129,164,578,1592,2951,4505,16826,17438,

%T 22748

%N Numbers k such that (316*10^k - 1)/9 is prime.

%C Numbers k such that the digits 35 followed by k occurrences of the digit 1 is prime (see Example section).

%C a(21) > 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 351w</a>.

%e 3 is in this sequence because (316*10^3 - 1)/9 = 35111 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 3511;

%e a(2) = 3, 35111;

%e a(3) = 8, 3511111111;

%e a(4) = 9, 35111111111;

%e a(5) = 11, 3511111111111; etc.

%t Select[Range[0, 100000], PrimeQ[(316*10^# - 1)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jul 21 2017