A295031 - OEIS

%I #11 May 11 2024 18:50:03

%S 2,4,5,14,28,34,209,398,482,904,1036,1748,2128,5998,7786,10402,18347,

%T 20806,33100

%N Numbers k such that (13*10^k + 311)/9 is prime.

%C Numbers k > 1 such that the digit 1 followed by k-2 occurrences of the digit 4 followed by the digits 79 is prime (see Example section).

%C a(20) > 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 14w79</a>.

%e 2 is in this sequence because (13*10^2 + 311)/9 = 179 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 179;

%e a(2) = 4, 14479;

%e a(3) = 5, 144479;

%e a(4) = 14, 144444444444479;

%e a(5) = 28, 14444444444444444444444444479; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 311)/9] &]

%o (PARI) isok(k) = isprime((13*10^k + 311)/9); \\ _Michel Marcus_, Nov 13 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 12 2017