|
%I #11 Jun 08 2024 15:47:53
%S 2,3,8,9,11,14,17,23,29,38,50,129,164,578,1592,2951,4505,16826,17438,
%T 22748
%N Numbers k such that (316*10^k - 1)/9 is prime.
%C Numbers k such that the digits 35 followed by k occurrences of the digit 1 is prime (see Example section).
%C a(21) > 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 351w</a>.
%e 3 is in this sequence because (316*10^3 - 1)/9 = 35111 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 3511;
%e a(2) = 3, 35111;
%e a(3) = 8, 3511111111;
%e a(4) = 9, 35111111111;
%e a(5) = 11, 3511111111111; etc.
%t Select[Range[0, 100000], PrimeQ[(316*10^# - 1)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Jul 21 2017
|
