A295624 - OEIS

%I #15 May 03 2024 18:44:17

%S 2,5,8,11,15,17,87,146,201,287,383,489,527,4077,5102,7769,22715,25077,

%T 37425,82161,180296

%N Numbers k such that (38*10^k + 403)/9 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 2 followed by the digits 67 is prime (see Example section).

%C a(22) > 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 42w67</a>.

%e 2 is in this sequence because (38*10^82 2 161+403)/9 = 467 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 467;

%e a(2) = 5, 422267;

%e a(3) = 8, 422222267;

%e a(4) = 11, 422222222267;

%e a(5) = 15, 4222222222222267; etc.

%t Select[Range[0, 100000], PrimeQ[(38*10^# + 403)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 24 2017

%E a(21) from _Robert Price_, Oct 03 2018