A291866 Numbers k such that (56*10^k + 691)/9 is prime.

0, 1, 3, 4, 6, 9, 15, 18, 36, 267, 294, 306, 321, 397, 828, 1501, 1723, 1905, 5047, 8413, 10273, 13519, 35569, 102255, 125385, 127752, 169311

Offset

1,3

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 62w99.

Example

3 is in this sequence because (56*10^3 + 691)/9 = 6299 is prime.
Initial terms and associated primes:
a(1) = 0, 83;
a(2) = 1, 139;
a(3) = 3, 6299;
a(4) = 4, 62299;
a(5) = 6, 6222299; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(56*10^# + 691)/9] &]

Crossrefs

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

Sequence in context: A048577 A107340 A326655 * A332829 A173270 A301657

Adjacent sequences: A291863 A291864 A291865 * A291867 A291868 A291869

Keyword

nonn,more,hard

Author

Robert Price, Sep 04 2017

Extensions

a(24)-a(27) from Robert Price, May 03 2019

Status

approved