A239717 Primes of the form m = 7^i + 7^j - 1, where i > j >= 0.

7, 349, 19207, 117991, 120049, 823591, 5765143, 5882449, 6588343, 40353949, 282475591, 2017680349, 2259801991, 13841289601, 14123762449, 96894775207, 96929364013, 678223072897, 678223075249, 4747567274743, 5425784582791

Offset: 1

Author

Hieronymus Fischer, Apr 14 2014

Keywords

• nonn

Comments

The base-7 representation of a term 7^i + 7^j - 1 has base-7 digital sum = 1 + 6*j == 1 (mod 6).

Numbers m that satisfy m = 7^i + 7^j + 1 are never primes, since the base-7 digital sum of m is 3, and thus, m is divisible by 3.

Examples

			a(1) = 7, since 7 = 7^1 + 7^0 - 1 is prime.
a(2) = 349, since 349 = 7^3 + 7^1 - 1 is prime.
		

Links

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

Programs

Mathematica

Select[Flatten[Table[7^x+7^y-1,{x,0,20},{y,0,x-1}]],PrimeQ] (* Harvey P. Dale, Aug 13 2023 *)

Smalltalk

A239717
  "Answers an array of the first n terms of A239717.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
  Usage: n A239717
  Answer: #(7 349 ... ) [a(1) ... a(n)]"
  ^self primesWhichAreDistinctPowersOf: 7 withOffset: -1