%I #11 Jun 09 2024 18:05:43

%S 0,1,3,4,6,9,15,18,36,267,294,306,321,397,828,1501,1723,1905,5047,

%T 8413,10273,13519,35569,102255,125385,127752,169311

%N Numbers k such that (56*10^k + 691)/9 is prime.

%C For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).

%C a(28) > 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 62w99</a>.

%e 3 is in this sequence because (56*10^3 + 691)/9 = 6299 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 83;

%e a(2) = 1, 139;

%e a(3) = 3, 6299;

%e a(4) = 4, 62299;

%e a(5) = 6, 6222299; etc.

%t Select[Range[0, 100000], PrimeQ[(56*10^# + 691)/9] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Sep 04 2017

%E a(24)-a(27) from _Robert Price_, May 03 2019