A295625 - OEIS

%I #12 May 03 2024 18:44:25

%S 0,1,7,12,16,18,37,67,82,90,133,622,624,1464,1963,4741,4824,13861,

%T 18423,61374

%N Numbers k such that (388*10^k - 1)/9 is prime.

%C For k > 1, numbers k such that the digits 43 followed by k occurrences of the digit 1 is prime (see Example section).

%C a(21) > 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 431w</a>.

%e 1 is in this sequence because (388*10^1 - 1)/9 = 431 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 43;

%e a(2) = 1, 431;

%e a(3) = 7, 431111111;

%e a(4) = 12, 43111111111111;

%e a(5) = 16, 431111111111111111; etc.

%t Select[Range[0, 100000], PrimeQ[(388*10^# - 1)/9] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 24 2017