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Numbers k such that (266*10^k - 11) / 3 is prime.
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%I #20 Jun 09 2024 18:06:32

%S 1,2,3,4,7,9,10,14,28,58,93,121,135,207,350,423,602,859,1026,1864,

%T 1966,13738,23299,28126,38691,39403,47499,93577,124022,177577

%N Numbers k such that (266*10^k - 11) / 3 is prime.

%C For k > 0, numbers k such that the digits 88 followed by k-1 occurrences of the digit 6 followed by the digit 3 is prime (see Example section).

%C a(31) > 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 886w3</a>.

%e 3 is in this sequence because (266*10^3 - 11) / 3 = 88663 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 883;

%e a(2) = 2, 8863;

%e a(3) = 3, 88663;

%e a(4) = 4, 886663;

%e a(5) = 7, 886666663, etc.

%t Select[Range[0, 100000], PrimeQ[(266*10^# - 11) / 3] &]

%o (PARI) is(n)=ispseudoprime((266*10^n - 11)/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 27 2016

%E a(29)-a(30) from _Robert Price_, Apr 01 2020