login
A338890
Numbers m such that m^2 = i^2 + 2*j^2 + k^2 and i^2 + j^2 and j^2 + k^2 are square numbers and i, j, k > 0.
2
25, 50, 75, 100, 125, 150, 169, 175, 200, 225, 250, 275, 289, 300, 325, 338, 350, 375, 377, 400, 425, 450, 475, 500, 507, 525, 550, 575, 578, 600, 625, 650, 675, 676, 700, 725, 750, 754, 769, 775, 797, 800, 825, 841, 845, 850, 867, 875, 900, 925, 950, 975
OFFSET
1,1
COMMENTS
All terms are hypotenuse numbers (A009003).
Each term is the hypotenuse of a Pythagorean triangle T whose legs, say u and v, are also the hypotenuses of Pythagorean triangles, say U and V, and U and V have a leg of the same length. This can be summarized as follows:
a(n)^2
/ \
/ \
/ T \
u^2-----v^2
/ \ / \
/ \ / \
/ U \ / V \
i^2-----j^2-----k^2
Any positive multiple of a term is also a term (see A338892 for the primitive terms).
LINKS
EXAMPLE
Regarding 169:
- we have 169^2 = 65^2 + 156^2, 65^2 = 25^2 + 60^2, 156^2 = 60^2 + 144^2:
169^2
/ \
/ \
/ \
65^2--156^2
/ \ / \
/ \ / \
/ \ / \
25^2---60^2----144^2
- so 169 belongs to the sequence.
PROG
(C#) See Links section.
CROSSREFS
Sequence in context: A085625 A116490 A230213 * A008607 A044077 A043350
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Nov 14 2020
STATUS
approved