%I #22 May 26 2024 14:58:41

%S 1,2,3,5,7,12,37,45,55,139,205,264,445,975,1111,1298,1340,1835,2264,

%T 2317,2897,2955,3001,4134,6637,7063,20613,114795,147890

%N Numbers k such that (17*10^k + 79)/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 93 is prime (see Example section).

%C a(30) > 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 56w93</a>.

%e 3 is in this sequence because (17*10^3+79)/3 = 5693 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 83;

%e a(2) = 2, 593;

%e a(3) = 3, 5693;

%e a(4) = 5, 566693;

%e a(5) = 7, 56666693, etc.

%t Select[Range[0, 100000], PrimeQ[(17*10^# + 79)/3] &]

%o (PARI) is(n)=ispseudoprime((17*10^n + 79)/3) \\ _Charles R Greathouse IV_, Jun 08 2016

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

%K nonn,more

%O 1,2

%A _Robert Price_, May 28 2016

%E a(28)-a(29) from _Robert Price_, Apr 15 2019