A283236 - OEIS

%I #12 Jun 09 2024 18:05:21

%S 1,2,7,22,50,76,77,130,193,259,347,590,665,838,1516,3512,3566,3688,

%T 5393,5408,5875,10160,24238,127967

%N Numbers k such that (86*10^k - 329)/9 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 5 followed by the digits 19 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 95w19</a>.

%e 2 is in this sequence because (86*10^2 - 329)/9 = 919 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 59;

%e a(2) = 2, 919;

%e a(3) = 7, 95555519;

%e a(4) = 22, 95555555555555555555519;

%e a(5) = 50, 955555555555555555555555555555555555555555555555519; etc.

%t Select[Range[1, 100000], PrimeQ[(86*10^# - 329)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Mar 03 2017

%E a(24) from _Robert Price_, Jan 11 2020