%I #16 May 26 2024 22:59:34

%S 1,3,6,9,12,18,24,31,36,39,57,91,129,529,798,1279,1728,6603,12883,

%T 29463,77811

%N Numbers k such that (13*10^k + 347)/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 83 is prime (see Example section).

%C a(22) > 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 14w83</a>.

%e 3 is in this sequence because (13*10^3 + 347)/9 = 1483 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 53;

%e a(2) = 3, 1483;

%e a(3) = 6, 1444483;

%e a(4) = 9, 1444444483;

%e a(5) = 12, 1444444444483; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 347)/9] &]

%o (PARI) isok(k) = isprime((13*10^k + 347)/9); \\ _Altug Alkan_, Oct 08 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 08 2017