A286176 Numbers k such that (209*10^k - 17)/3 is prime.

1, 2, 3, 7, 13, 14, 37, 38, 54, 60, 69, 668, 693, 825, 1275, 1566, 3129, 5745, 6439, 21991, 24992, 61947, 96722

Offset

1,2

Comments

For k > 0, numbers k such that the digits 69 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 696w1.

Example

3 is in this sequence because (209*10^3 - 17)/3 = 69661 is prime.
Initial terms and associated primes:
a(1) = 1, 691;
a(2) = 2, 6961;
a(3) = 3, 69661;
a(4) = 7, 696666661;
a(5) = 13, 696666666666661; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(209*10^# - 17)/3] &]

Crossrefs

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

Sequence in context: A084955 A273056 A026472 * A318401 A322703 A225098

Adjacent sequences: A286173 A286174 A286175 * A286177 A286178 A286179

Keyword

nonn,more,hard

Author

Robert Price, May 03 2017

Status

approved