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Numbers k such that (25*10^k - 37) / 3 is prime.
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%I #16 Jun 09 2024 18:06:20

%S 1,2,7,17,24,32,66,67,74,92,104,117,188,260,279,336,348,369,547,619,

%T 860,2735,7932,11874,14867,40153,171849,176715

%N Numbers k such that (25*10^k - 37) / 3 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 21 is prime (see Example section).

%C a(29) > 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 83w21</a>.

%e 2 is in this sequence because (25*10^2 - 37) / 3 = 821 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 71;

%e a(2) = 2, 821;

%e a(3) = 7, 83333321;

%e a(4) = 17, 833333333333333321;

%e a(5) = 24, 8333333333333333333333321, etc.

%t Select[Range[0, 100000], PrimeQ[(25*10^# - 37) / 3] &]

%o (PARI) is(n)=ispseudoprime((25*10^n - 37)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, Sep 14 2016

%E a(27)-a(28) from _Robert Price_, Oct 07 2019