A294942 - OEIS

%I #14 May 11 2024 19:12:13

%S 0,2,6,15,18,26,51,75,86,114,257,275,537,753,914,1944,18431,18741,

%T 21281,28272,31002,71621,84170,110961

%N Numbers k such that (74*10^k + 313)/9 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 2 followed by the digits 57 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 82w57</a>.

%e 2 is in this sequence because (74*10^2 + 313)/9 = 857 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 2, 857;

%e a(3) = 6, 8222257;

%e a(4) = 15, 8222222222222257;

%e a(5) = 18, 8222222222222222257; etc.

%t Select[Range[0, 100000], PrimeQ[(74*10^# + 313)/9] &]

%o (PARI) isok(k) = isprime((74*10^k + 313)/9); \\ _Michel Marcus_, Nov 12 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 11 2017

%E a(24) from _Robert Price_, Jun 14 2019