A281275 - OEIS

%I #13 May 25 2024 14:23:34

%S 1,2,4,7,8,14,19,34,40,55,178,251,314,410,982,1198,1604,2486,2642,

%T 3928,19231,24874,28850,143963

%N Numbers k such that (19*10^k + 467)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 1 followed by the digits 63 is prime (see Example section).

%C a(25) > 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 21w63</a>.

%e 2 is in this sequence because (19*10^2 + 467)/9 = 263 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 73;

%e a(2) = 2, 263;

%e a(3) = 4, 21163;

%e a(4) = 7, 21111163;

%e a(5) = 8, 211111163; etc.

%t Select[Range[0, 100000], PrimeQ[(19*10^# + 467)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 18 2017

%E a(24) from _Robert Price_, Feb 14 2018