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Numbers k such that (68*10^k - 257)/9 is prime.
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%I #11 Jun 02 2024 20:58:55

%S 1,2,4,8,11,20,22,32,40,62,95,104,569,710,955,1682,2933,4592,10286,

%T 16634,19235,20437,31024,48304,79813,128645,148060

%N Numbers k such that (68*10^k - 257)/9 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 5 followed by the digits 27 is prime (see Example section).

%C a(28) > 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 75w27</a>.

%e 4 is in this sequence because (68*10^4 - 257)/9 = 75527 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 47;

%e a(2) = 2, 727;

%e a(3) = 4, 75527;

%e a(4) = 8, 755555527;

%e a(5) = 11, 755555555527; etc.

%t Select[Range[1, 100000], PrimeQ[(68*10^# - 257)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jun 05 2017

%E a(26)-a(27) from _Robert Price_, Jul 27 2019