A239714 Primes of the form m = 4^i + 4^j - 1, where i > j >= 0.

19, 67, 79, 271, 1039, 1087, 1279, 4099, 4111, 4159, 5119, 16447, 20479, 65539, 65551, 65599, 81919, 262147, 262399, 263167, 266239, 1049599, 1114111, 1310719, 4194319, 4194559, 4195327, 16842751, 17825791, 67108879, 268435459, 268435711, 272629759, 1073741827, 1073741839, 1073758207

Offset

1,1

Comments

The base-4 representation of a term 4^i + 4^j - 1 has base-4 digital sum = 1 + 3*j == 1 (mod 3).

In base-4 representation the first terms are 103, 1003, 1033, 10033, 100033, 100333, 103333, 1000003, 1000033, 1000333, 1033333, 10000333, 10333333, 100000003, 100000033, 100000333, 103333333, 1000000003, 1000003333, 1000033333, ...

Numbers m which satisfy m = 4^i + 4^j + 1 are never primes, since the base-4 digital sum of m is 3, and thus, m is divisible by 3.

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..111

Example

a(1) = 19, since 19 = 4^2 + 4^1 - 1 is prime.
a(4) = 271, since 271 = 4^4 + 4^2 - 1 is prime.

Prog

(Smalltalk)
A239714
  "Answer an array of the first n terms of A239714.
  Uses method primesWhichAreDistinctPowersOf: b withOffset: d from A239712.
  Usage: n A239714
  Answer: #(19 67 79 ... ) [a(1) ... a(n)]"
  ^self primesWhichAreDistinctPowersOf: 4 withOffset: -1

Crossrefs

Cf. A234310.

Sequence in context: A156967 A244146 A104047 * A201781 A165806 A357676

Adjacent sequences: A239711 A239712 A239713 * A239715 A239716 A239717

Keyword

nonn

Author

Hieronymus Fischer, Apr 14 2014

Status

approved