A287685 Numbers k such that 89*10^k - 9 is prime.

1, 7, 13, 44, 73, 128, 152, 245, 408, 436, 618, 638, 884, 1405, 1502, 1656, 2292, 2318, 4212, 5712, 5868, 13837, 18648, 25102, 30742, 34532, 53951, 159258

Offset

1,2

Comments

For k>0, numbers such that the digits 88 followed by k-1 occurrences of the digit 9 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 889w1.

Example

7 is in this sequence because 89*10^7 - 9 = 889999991 is prime.
Initial terms and primes associated:
a(1) = 1, 881;
a(2) = 7, 889999991;
a(3) = 13, 889999999999991;
a(4) = 44, 8899999999999999999999999999999999999999999991;  etc.

Mathematica

Select[Range[0, 100000], PrimeQ[89*10^# - 9] &]

Crossrefs

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

Sequence in context: A087820 A272032 A023286 * A159305 A146648 A219501

Adjacent sequences: A287682 A287683 A287684 * A287686 A287687 A287688

Keyword

nonn,more,hard

Author

Robert Price, May 29 2017

Extensions

a(28) from Robert Price, May 12 2020

Status

approved