A294939 - OEIS

%I #14 May 11 2024 19:12:04

%S 0,1,2,3,5,8,13,69,80,344,405,500,794,926,3293,3964,7203,7395,8163,

%T 14433,68455,108273,137845

%N Numbers k such that (8*10^k + 13)/3 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 6 followed by the digits 71 is prime (see Example section).

%C a(24) > 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 26w71</a>.

%e 2 is in this sequence because (8*10^2 + 13)/3 = 271 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 7;

%e a(2) = 1, 31;

%e a(3) = 2, 271;

%e a(4) = 3, 2671;

%e a(5) = 5, 266671; etc.

%t Select[Range[0, 100000], PrimeQ[(8*10^# + 13)/3] &]

%o (PARI) isok(k) = isprime((8*10^k + 13)/3); \\ _Michel Marcus_, Nov 12 2017

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 11 2017

%E a(22)-a(23) from _Robert Price_, Jun 12 2018