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Numbers k such that (13*10^k + 179)/3 is prime.
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%I #15 May 25 2024 16:58:13

%S 1,5,8,21,37,61,62,126,188,221,253,523,654,1875,2372,2394,3073,4158,

%T 6663,6881,167911

%N Numbers k such that (13*10^k + 179)/3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 93 is prime (see Example section).

%C a(22) > 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 43w93</a>.

%e 5 is in this sequence because (13*10^5 + 179)/3 = 433393 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 103;

%e a(2) = 5, 433393;

%e a(3) = 8, 433333393;

%e a(4) = 21, 4333333333333333333393;

%e a(5) = 37, 43333333333333333333333333333333333393; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 179)/3] &] (* corrected by _Georg Fischer_, Jul 22 2019 *)

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 23 2017

%E a(21) from _Robert Price_, Nov 17 2018