A287296 Numbers k such that 8*10^k + 51 is prime.

0, 1, 4, 6, 9, 10, 16, 31, 33, 93, 289, 304, 921, 1183, 3946, 4506, 4978, 5481, 7114, 13512, 14703, 14823, 16851, 26662, 77377, 82417, 95316, 98982, 102000, 139920

Offset

1,3

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 0 followed by the digits 51 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 80w51.

Example

4 is in this sequence because 8*10^4 + 51 = 80051 is prime.
Initial terms and associated primes:
a(1) = 0, 59;
a(2) = 1, 131;
a(3) = 4, 80051;
a(4) = 6, 8000051;
a(5) = 9, 8000000051; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[8*10^# + 51] &]

Crossrefs

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

Sequence in context: A087112 A077554 A262812 * A275197 A118778 A108635

Adjacent sequences: A287293 A287294 A287295 * A287297 A287298 A287299

Keyword

nonn,more,hard

Author

Robert Price, May 22 2017

Extensions

a(29)-a(30) from Robert Price, Aug 18 2019

Terms reordered into ascending order by Robert Price, Apr 03 2022

Status

approved