A286395 Numbers k such that (17*10^k + 67)/3 is prime.

1, 3, 7, 8, 9, 11, 15, 19, 29, 55, 76, 159, 266, 311, 394, 908, 1732, 1875, 4335, 6334, 7641, 16421, 33721, 139239, 157705, 160143

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 89 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 56w89.

Example

3 is in this sequence because (17*10^3 + 67)/3 = 5689 is prime.
Initial terms and associated primes:
a(1) = 1, 79;
a(2) = 3, 5689;
a(3) = 7, 56666689;
a(4) = 8, 566666689;
a(5) = 9, 5666666689; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(17*10^# + 67)/3] &]

Crossrefs

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

Sequence in context: A346300 A265350 A096315 * A112680 A096079 A298984

Adjacent sequences: A286392 A286393 A286394 * A286396 A286397 A286398

Keyword

nonn,more,hard

Author

Robert Price, May 09 2017

Extensions

a(24)-a(26) from Robert Price, Jan 24 2019

Status

approved