%I #12 Jun 07 2024 23:59:08

%S 1,2,4,5,7,8,11,13,20,22,38,47,76,269,299,527,724,1214,2243,2327,

%T 12635,15064,28921,34303,49117,58151,89279,199283

%N Numbers k such that (2*10^k + 457)/9 is prime.

%C For k > 2, numbers k such that k-2 occurrences of the digit 2 followed by the digits 73 is prime (see Example section).

%C a(29) > 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 2w73</a>.

%e 2 is in this sequence because (2*10^2 + 457) / 9 = 73 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 53;

%e a(2) = 2, 73;

%e a(3) = 4, 2273;

%e a(4) = 5, 22273;

%e a(5) = 7, 2222273; etc.

%t Select[Range[0, 100000], PrimeQ[(2*10^# + 457) / 9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 18 2017

%E a(28) from _Robert Price_, Jan 08 2018