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Numbers k such that (25*10^k - 67)/3 is prime.
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%I #36 May 25 2024 13:53:35

%S 1,2,3,4,39,63,64,82,129,441,685,947,1042,1063,1840,2311,8200,9641,

%T 15982,17643,45389,54443,100343,102076,124076

%N Numbers k such that (25*10^k - 67)/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 11 is prime (see Example section).

%C a(26) > 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 83w11</a>.

%e 2 is in this sequence because (25*10^2 - 67)/3 = 811 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 61;

%e a(2) = 2, 811;

%e a(3) = 3, 8311;

%e a(4) = 4, 83311;

%e a(5) = 39, 8333333333333333333333333333333333333311; etc.

%t Select[Range[1, 100000], PrimeQ[(25*10^# - 67)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 10 2017

%E a(23)-a(25) from _Robert Price_, Jun 19 2019