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Numbers k such that (184*10^k - 1)/3 is prime.
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%I #18 Jun 08 2024 15:47:45

%S 0,1,2,3,21,24,25,39,42,90,192,547,3185,3363,4279,4496,4761,5022,6807,

%T 13220,13283,13519,25183,37609,84348,87473,112007,211682

%N Numbers k such that (184*10^k - 1)/3 is prime.

%C Numbers k such that the digits 61 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(29) > 3*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 613w</a>.

%e 2 is in this sequence because (184*10^2 - 1)/3 = 6133 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 61;

%e a(2) = 1, 613;

%e a(3) = 2, 6133;

%e a(4) = 3, 61333;

%e a(5) = 21, 61333333333333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(184*10^# - 1)/3] &]

%o (PARI) isok(k) = isprime((184*10^k - 1)/3); \\ _Michel Marcus_, Feb 12 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Feb 12 2017

%E a(27) from _Robert Price_, Feb 26 2020

%E a(28) from _Robert Price_, Jul 02 2023