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Numbers k such that (32*10^k - 77)/9 is prime.
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%I #11 May 25 2024 19:36:54

%S 2,3,8,12,15,75,92,123,126,267,272,525,561,1041,1947,2571,11667,13656,

%T 15981,29852,35256,105530,122733,125751

%N Numbers k such that (32*10^k - 77)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).

%C a(25) > 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 35w47</a>.

%e 3 is in this sequence because (32*10^3 - 77)/9 = 3547 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 347;

%e a(2) = 3, 3547;

%e a(3) = 8, 355555547;

%e a(4) = 12; 3555555555547;

%e a(5) = 15, 3555555555555547; etc.

%t Select[Range[1, 100000], PrimeQ[(32*10^# - 77)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jul 21 2017

%E a(22)-a(24) from _Robert Price_, Jun 10 2018