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Numbers k such that (26*10^k - 77)/3 is prime.
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%I #39 Jun 10 2024 08:43:40

%S 1,3,5,7,11,12,15,27,36,108,110,115,127,155,958,2782,3090,6520,9857,

%T 14543,21919,23659,24727,49039,92546,114317,131180,146856,204730,

%U 219639,238157

%N Numbers k such that (26*10^k - 77)/3 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 41 is prime (see Example section).

%C a(32) > 3*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 86w41</a>.

%e 3 is in this sequence because (26*10^3 - 77)/3 = 8641 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 61;

%e a(2) = 3, 8641;

%e a(3) = 5, 866641;

%e a(4) = 7, 86666641;

%e a(5) = 11, 866666666641; etc.

%t Select[Range[1, 100000], PrimeQ[(26*10^# - 77)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 22 2017

%E a(26)-a(28) from _Robert Price_, Nov 15 2019

%E a(29)-a(31) from _Robert Price_, Jul 12 2023