%I #15 May 03 2024 07:45:59

%S 1,2,5,8,32,37,38,53,104,128,241,866,872,943,1058,4351,16471,16925,

%T 23933,43511,73079,105811

%N Numbers k such that (5*10^k + 211)/9 is prime.

%C For k > 1, numbers k such that k-2 occurrences of the digit 5 followed by the digits 79 is prime (see Example section).

%C a(23) > 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 5w79</a>.

%e 2 is in this sequence because (5*10^2 + 211)/9 = 79 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 29;

%e a(2) = 2, 79;

%e a(3) = 5, 55579;

%e a(4) = 8, 55555579;

%e a(5) = 32, 55555555555555555555555555555579; etc.

%t Select[Range[0, 100000], PrimeQ[(5*10^# + 211)/9] &]

%o (PARI) isok(k) = isprime((5*10^k + 211)/9); \\ _Michel Marcus_, Dec 01 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 30 2017

%E a(22) from _Robert Price_, Feb 14 2018