A282351 - OEIS

%I #13 Jun 08 2024 05:44:16

%S 2,3,6,14,17,29,41,44,87,213,354,840,972,1263,2018,2534,4868,7992,

%T 13676,18354,19304,40515,126638,135279

%N Numbers k such that (13*10^k + 437)/9 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 4 followed by the digits 93 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 14w93</a>.

%e 3 is in this sequence because (13*10^3 + 437)/9 = 1493 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 193;

%e a(2) = 3, 1493;

%e a(3) = 6, 1444493;

%e a(4) = 14, 144444444444493;

%e a(5) = 17, 144444444444444493; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 437)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Feb 12 2017

%E a(23)-a(24) from _Robert Price_, Apr 14 2018