A280019 - OEIS

%I #16 Jun 09 2024 22:16:23

%S 1,2,3,5,10,23,29,56,68,199,364,436,478,1178,1187,1869,4733,11816,

%T 11867,17383,27987,42005,51889,111770,113176,168541

%N Numbers k such that (94*10^k + 11)/3 is prime.

%C For k > 1, numbers k such that the digits 31 followed by k-1 occurrences of the digit 3 followed by the digit 7 is prime (see Example section).

%C a(27) > 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 313w7</a>.

%e 3 is in this sequence because (94*10^3 + 11)/3 = 31337 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 317;

%e a(2) = 2, 3137;

%e a(3) = 3, 31337;

%e a(4) = 5, 3133337;

%e a(5) = 10, 313333333337; etc.

%t Select[Range[0, 100000], PrimeQ[(94*10^# + 11)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 21 2017

%E a(24)-a(26) from _Robert Price_, Apr 03 2020