A281063 Numbers k such that (299*10^k - 17)/3 is prime.

1, 3, 6, 12, 16, 18, 27, 30, 59, 60, 61, 118, 198, 208, 826, 1696, 1813, 4505, 7111, 9715, 11572, 15439, 17406, 55998, 89836, 158544, 199801, 201547

Offset

1,2

Comments

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

a(29) > 3*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 996w1.

Example

3 is in this sequence because (299*10^3 - 17) / 3 = 99661 is prime.
Initial terms and associated primes:
a(1) = 1, 991;
a(2) = 3, 99661;
a(3) = 6, 99666661;
a(4) = 12, 99666666666661;
a(5) = 16, 996666666666666661; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(299*10^# - 17) / 3] &]

Crossrefs

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

Sequence in context: A390294 A267353 A320607 * A032602 A116593 A109735

Adjacent sequences: A281060 A281061 A281062 * A281064 A281065 A281066

Keyword

nonn,more,hard

Author

Robert Price, Jan 13 2017

Extensions

a(26)-a(27) from Robert Price, Apr 15 2020

Constant 229 corrected to 299 by Georg Fischer, Jun 26 2020

a(28) from Robert Price, Jun 21 2023

Status

approved