|
%I #37 Jun 10 2024 23:36:14
%S 2,3,4,5,8,9,16,17,18,36,54,69,183,200,240,846,1424,2511,4750,13854,
%T 15414,103450,128094,132746
%N Numbers k such that (22*10^k + 53)/3 is prime.
%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 3 followed by the digits 51 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 73w51</a>.
%e 3 is in this sequence because (22*10^3 + 53)/3 = 7351 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 751;
%e a(2) = 3, 7351;
%e a(3) = 4, 73351;
%e a(4) = 5, 733351;
%e a(5) = 8, 733333351; etc.
%t Select[Range[0, 100000], PrimeQ[(22*10^# + 53)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, May 09 2017
%E a(22)-a(24) from _Robert Price_, Jul 06 2019
|
