|
%I #12 Jun 06 2024 23:23:36
%S 0,1,2,4,7,40,43,74,98,181,186,428,532,644,1664,2016,2476,2911,2959,
%T 3007,5964,7758,22231,92152
%N Numbers k such that (2*10^k + 67)/3 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 6 followed by the digits 89 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 6w89</a>.
%e 4 is in this sequence because (2*10^4 + 67)/3 = 6689 is prime.
%e Initial terms and associated primes:
%e a(1) = 0, 23;
%e a(2) = 1, 29;
%e a(3) = 2, 89;
%e a(4) = 4, 6689;
%e a(5) = 7, 6666689; etc.
%t Select[Range[0, 100000], PrimeQ[(2*10^# + 67)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard,changed
%O 1,3
%A _Robert Price_, Apr 29 2017
|
