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Numbers k such that (379*10^k - 1)/9 is prime.
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%I #16 Jun 09 2024 18:05:39

%S 1,2,5,8,10,11,20,56,161,172,263,290,578,800,1166,3382,3848,7036,

%T 10487,12101,36211,94337,138737

%N Numbers k such that (379*10^k - 1)/9 is prime.

%C For k > 0, numbers k such that the digits 42 followed by k occurrences of the digit 1 is prime (see Example section).

%C a(24) > 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 421w</a>.

%e 2 is in this sequence because (379*10^2 - 1)/9 = 4211 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 421;

%e a(2) = 2, 4211;

%e a(3) = 5, 4211111;

%e a(4) = 8; 4211111111;

%e a(5) = 10, 421111111111; etc.

%t Select[Range[0, 100000], PrimeQ[(379*10^# - 1)/9] &]

%o (PARI) isok(k) = isprime((379*10^k - 1)/9); \\ _Michel Marcus_, Aug 07 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 06 2017

%E a(23) from _Robert Price_, Feb 14 2020