A239718 Primes of the form m = 8^i + 8^j - 1, where i > j >= 0.

71, 4159, 32831, 262151, 266239, 294911, 2101247, 18874367, 134479871, 1073741831, 68721573887, 549755813951, 4398046515199, 4398046543871, 4398046773247, 4398063288319, 281474976711167, 281474976743423, 281474978807807, 281474993487871, 282024732524543

Offset

1,1

Comments

The base-8 representation of a term 8^i + 8^j - 1 has base-8 digital sum = 1 + 7*j == 1 (mod 7).

In base-8 representation the first terms are 107, 10077, 100077, 1000007, 1007777, 1077777, 10007777, 107777777, 1000777777, 10000000007, 1000007777777, 10000000000077, 100000000007777, ...

Numbers m that satisfy m = 8^i + 8^j - 1 with odd i and j are not terms. Example: 33279 = 8^5 + 8^3 - 1 = 3*11093.

Links

Georg Fischer, Table of n, a(n) for n = 1..40 [First 35 terms from Hieronymus Fischer]

Example

a(1) = 71, since 71 = 8^2 + 8^1 - 1 is prime.
a(2) = 4159, since 4159 = 8^4 + 8^2 - 1 is prime.

Maple

select(isprime, [seq(seq(8^i+8^j-1, j=0..i-1), i=1..25)])[];  # Alois P. Heinz, Dec 22 2024

Prog

(Smalltalk)
A239718
  "Answers an array of the first n terms of A239718.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
Usage: n A239718
Answer: #(71 4159 ... ) [a(1) ... a(n)]"
  ^self primesWhichAreDistinctPowersOf: 8 withOffset: -1

Crossrefs

Cf. A018900, A239709, A239712 (base 2), A239713 (base 3), A239714 (base 4), A239715 (base 5), A239716 (base 6), A239717 (base 7), A239719 (base 9), A239720 (base 10).

Sequence in context: A017734 A263248 A221051 * A279904 A115447 A200960

Adjacent sequences: A239715 A239716 A239717 * A239719 A239720 A239721

Keyword

nonn

Author

Hieronymus Fischer, Apr 14 2014

Status

approved