A306103 Numbers that are the difference of two positive squares in at least three ways.

45, 48, 63, 72, 75, 80, 96, 99, 105, 112, 117, 120, 128, 135, 144, 147, 153, 160, 165, 168, 171, 175, 176, 180, 189, 192, 195, 200, 207, 208, 216, 224, 225, 231, 240, 243, 245, 252, 255, 256, 261, 264, 272, 273, 275, 279, 280, 285, 288, 297, 300

Offset

1,1

Comments

Numbers n such that A100073(n) >= 3; see there for more information & formulas.

Links

Metin Sariyar, Table of n, a(n) for n = 1..10000

Geoffrey Campbell, Numbers that are the difference of two squares in two or more ways, Number Theory Group on LinkedIn, July 8, 2018.

Formula

A306103 = { n = 2k+1 | A056924(n) > 2 } U { n = 4k | A056924(n/4) > 2 }.

Example

48 = 7^2 - 1^2 = 8^2 - 4^2 = 13^2 - 11^2.

Mathematica

Select[Range[300], Length[FindInstance[x^2 - y^2 == # && x>y>0, {x, y}, Integers, 3 ]] == 3 &] (* Giovanni Resta, Jul 10 2018 *)

Prog

(PARI) select( is(n)=A100073(n)>2, [1..300])

Crossrefs

Cf. A100073, A058957, A056924.

Subsequence of A306102. Contains A306104 as a subsequence.

Sequence in context: A291788 A291787 A257410 * A045566 A274368 A214572

Adjacent sequences: A306100 A306101 A306102 * A306104 A306105 A306106

Keyword

nonn

Author

Geoffrey B. Campbell and M. F. Hasler, Jul 10 2018

Status

approved