%I #19 May 25 2024 19:08:44

%S 1,2,3,4,6,10,11,24,53,83,97,156,157,162,182,233,355,499,629,1252,

%T 6378,8366,26406,35345,107694,126784,195234,255805

%N Numbers k such that (14*10^k - 83)/3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 6 followed by the digits 39 is prime (see Example section).

%C a(29) > 3*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 46w39</a>.

%e 4 is in this sequence because (14*10^4 - 83) / 3 = 46639 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 19;

%e a(2) = 2, 439;

%e a(3) = 3, 4639;

%e a(4) = 4, 46639;

%e a(5) = 6, 4666639; etc.

%t Select[Range[1, 100000], PrimeQ[(14*10^# - 83) / 3] &]

%o (PARI) is(n)=ispseudoprime((14*10^n - 83)/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(25)-a(27) from _Robert Price_, Dec 23 2018

%E a(28) from _Robert Price_, Jun 17 2023