A293399 Numbers k such that (68*10^k - 11)/3 is prime.

0, 1, 4, 6, 9, 20, 57, 64, 88, 196, 265, 421, 620, 654, 729, 1587, 4863, 6628, 12358, 23773, 68798, 119931

Offset

1,3

Comments

For k > 0, numbers k such that the digits 22 followed by k-1 occurrences of the digit 6 followed by the digit 3 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 226w3.

Example

1 is in this sequence because (68*10^1 - 11)/3 = 223 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 223;
a(3) = 4, 226663;
a(4) = 6, 22666663;
a(5) = 9, 22666666663; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(68*10^# - 11)/3] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

Prog

(PARI) isok(k) = isprime((68*10^k - 11)/3); \\ Altug Alkan, Oct 08 2017

Crossrefs

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

Sequence in context: A152002 A171127 A098485 * A120712 A115698 A039566

Adjacent sequences: A293396 A293397 A293398 * A293400 A293401 A293402

Keyword

nonn,more,hard

Author

Robert Price, Oct 08 2017

Extensions

a(22) from Robert Price, Jan 07 2020

Status

approved