A295324 Numbers k such that (17*10^k - 89)/9 is prime.

2, 3, 6, 12, 39, 45, 50, 75, 126, 282, 431, 459, 1557, 2724, 3453, 4058, 15879, 24209, 31844, 61760, 155133

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 8 followed by the digits 79 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

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

Makoto Kamada, Search for 18w79.

Example

2 is in this sequence because (17*10^2 - 89)/9 = 179 is prime.
Initial terms and associated primes:
a(1) = 2, 179;
a(2) = 3, 1879;
a(3) = 6, 1888879;
a(4) = 12, 1888888888879;
a(5) = 39, 1888888888888888888888888888888888888879; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(17*10^# - 89)/9] &]

Prog

(PARI) isok(k) = isprime((17*10^k - 89)/9); \\ Michel Marcus, Nov 20 2017

Crossrefs

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

Sequence in context: A102970 A144771 A187013 * A054049 A276690 A175281

Adjacent sequences: A295321 A295322 A295323 * A295325 A295326 A295327

Keyword

nonn,more,hard

Author

Robert Price, Nov 19 2017

Extensions

a(21) from Robert Price, Jul 23 2018

Status

approved