A239719 Primes of the form m = 9^i + 9^j - 1, where i > j >= 0.

89, 809, 6569, 65609, 531521, 538001, 590489, 4782977, 4783697, 47829689, 3486784409, 3491567369, 3529831121, 31768480097, 34867844009, 282430067921, 285916320881, 313810596089, 2541865834889, 22877179875449, 25418658283289

Offset: 1

Author

Hieronymus Fischer, Apr 14 2014

Keywords

• nonn

Comments

The base-9 representation of a term 9^i + 9^j - 1 has base-9 digital sum = 1 + 8*j == 1 (mod 8).

In base-9 representation the first terms are 108, 1088, 10008, 108888, 1000088, 1008888, 1088888, 10000008, 10000888, 108888888, 10000000008, 10008888888, 10088888888, 100888888888, ...

Examples

			a(1) = 89, since 89 = 9^2 + 9^1 - 1 is prime.
a(2) = 809, since 809 = 9^3 + 9^2 - 1 is prime.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..40

Programs

Mathematica

Select[Flatten[Table[9^i+9^j-1,{i,0,20},{j,0,i-1}]],PrimeQ] (* Harvey P. Dale, Jun 02 2023 *)

Smalltalk

A239719
  "Answer an array of the first n terms of A239719.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
  Usage: n A239719
  Answer: #(89 809 ... ) [a(1) ... a(n)]"
  ^self primesWhichAreDistinctPowersOf: 9 withOffset: -1