A273944 - OEIS

%I #40 May 02 2024 04:28:02

%S 0,1,2,3,7,8,11,14,24,29,50,78,99,192,226,519,613,651,1492,3720,6567,

%T 6791,7226,8471,9050,13521,14255,33529,44072,47844,64102,112930,

%U 116024,122872,138328,140681,268407

%N Numbers k such that (266*10^k - 17)/3 is prime.

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

%C a(38) > 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 886w1</a>.

%e 3 is in this sequence because (266*10^3-17)/3 = 88661 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 83;

%e a(2) = 1, 881;

%e a(3) = 2, 8861;

%e a(4) = 3, 88661;

%e a(5) = 7, 886666661, etc.

%t Select[Range[0, 100000], PrimeQ[(266*10^# - 17)/3] &]

%o (PARI) isok(n) = isprime((266*10^n - 17)/3); \\ _Michel Marcus_, Jun 18 2016

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

%K nonn,more

%O 1,3

%A _Robert Price_, Jun 17 2016

%E a(32)-a(36) from _Robert Price_, Jul 16 2020

%E a(37) from _Robert Price_, Jun 21 2023