A295522 - OEIS

%I #44 May 03 2024 18:44:09

%S 0,1,2,8,18,24,96,152,204,296,566,703,1814,4342,4626,5412,6704,6752,

%T 7096,27004,37976,173251

%N Numbers k such that (16*10^k + 107)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 69 is prime (see Example section).

%C a(23) > 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 53w69</a>.

%e 2 is in this sequence because (16*10^2 + 107)/3 = 569 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 41;

%e a(2) = 1, 89;

%e a(3) = 2, 569;

%e a(4) = 8, 533333369;

%e a(5) = 18, 5333333333333333369; etc.

%t Select[Range[0, 100000], PrimeQ[(16*10^# + 107)/3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Nov 28 2017

%E a(22) from _Robert Price_, Mar 06 2019