A280381 - OEIS

%I #20 Jun 08 2024 00:00:37

%S 1,2,5,6,8,12,13,14,19,61,127,137,173,175,305,540,617,935,1398,1834,

%T 3295,4351,9188,10808,39409,57325,63798,67091,183764,194502,196921,

%U 288692

%N Numbers k such that (17*10^k + 31)/3 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 77 is prime (see Example section).

%C a(33) > 3*10^5. - _Robert Price_, Jul 10 2023

%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 56w77</a>.

%e 5 is in this sequence because (17*10^5 + 31) / 3 = 566677 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 67;

%e a(2) = 2, 577;

%e a(3) = 5, 566677;

%e a(4) = 6, 5666677;

%e a(5) = 8, 5333333333351; etc.

%t Select[Range[0, 100000], PrimeQ[(17*10^# + 31) / 3] &]

%o (PARI) is(n)=ispseudoprime((17*10^n + 31)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Jan 01 2017

%E a(29)-a(31) from _Robert Price_, Jan 29 2019

%E a(32) from _Robert Price_, Jul 10 2023