A294911 Numbers k such that (299*10^k + 1)/3 is prime.

1, 2, 3, 5, 6, 8, 11, 12, 36, 63, 79, 152, 159, 236, 365, 542, 734, 2552, 9407, 31832, 32028, 43217, 51139, 58893, 71963, 190533, 197426, 278546

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 7 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 996w7.

Example

2 is in this sequence because (299*10^2 + 1)/3 = 9967 is prime.
Initial terms and associated primes:
a(1) = 1, 997;
a(2) = 2, 9967;
a(3) = 3, 99667;
a(4) = 5, 9966667;
a(5) = 6, 99666667; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(299*10^# + 1)/3] &]

Crossrefs

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

Sequence in context: A161720 A105760 A050834 * A179799 A247588 A275341

Adjacent sequences: A294908 A294909 A294910 * A294912 A294913 A294914

Keyword

nonn,more,hard

Author

Robert Price, Nov 10 2017

Extensions

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

a(28) from Robert Price, Jun 21 2023

Status

approved