A289942 - OEIS

%I #19 Jun 02 2024 14:05:41

%S 1,2,5,9,64,69,118,377,409,616,959,1093,1726,3034,5929,8140,11197,

%T 15293,15381,27811,58091,63757,72025,83921,122585,139913,166297,256301

%N Numbers k such that (85*10^k - 1)/3 is prime.

%C Numbers k such that the digits 28 followed by k occurrences of the digit 3 is prime (see Example section).

%C a(29) > 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 283w</a>.

%e 2 is in this sequence because (85*10^2 - 1)/3 = 2833 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 283;

%e a(2) = 2, 2833;

%e a(3) = 5, 2833333;

%e a(4) = 9, 28333333333;

%e a(5) = 64, 283333333333333333333333333333333333333333333333333333333333333333; etc.

%t Select[Range[0, 100000], PrimeQ[(85*10^# - 1)/3] &]

%o (PARI) isok(k) = isprime((85*10^k - 1)/3); \\ _Michel Marcus_, Jul 16 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jul 15 2017

%E a(25)-a(27) from _Robert Price_, Feb 03 2020

%E a(28) from _Robert Price_, Jul 02 2023