A288150 - OEIS

%I #12 Jun 10 2024 23:36:10

%S 4,8,11,12,16,20,22,34,35,38,51,52,106,135,168,189,194,224,482,3456,

%T 4832,36022,52119

%N Numbers k such that (25*10^k + 23)/3 is prime.

%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 41 is prime (see Example section).

%C a(24) > 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 83w41</a>.

%e 4 is in this sequence because (25*10^4 + 23)/3 = 83341 is prime.

%e Initial terms and associated primes:

%e a(1) = 4, 83341;

%e a(2) = 8, 833333341;

%e a(3) = 11, 833333333341;

%e a(4) = 12, 8333333333341;

%e a(5) = 16, 83333333333333341; etc.

%t Select[Range[0, 100000], PrimeQ[(25*10^# + 23)/3] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jun 05 2017