A279549 - OEIS

%I #28 Jun 02 2024 20:58:30

%S 1,2,3,9,10,14,36,44,69,124,249,297,453,535,766,1074,1668,1975,1987,

%T 2295,5703,6526,13329,34738,37549,39825,93236,99508,136687

%N Numbers k such that (13*10^k + 47) / 3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 49 is prime (see Example section).

%C a(30) > 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 43w49</a>.

%e 3 is in this sequence because (13*10^3 + 47) / 3 = 4349 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 59;

%e a(2) = 2, 449;

%e a(3) = 3, 4349;

%e a(4) = 9, 4333333349;

%e a(5) = 10, 43333333349; etc.

%t Select[Range[0, 100000], PrimeQ[(13*10^# + 47) / 3] &]

%o (PARI) is(n)=ispseudoprime((13*10^n + 47)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 05 2017

%E a(29) from _Robert Price_, Oct 14 2018