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.

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

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C# program for A338890

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

Cf. A009003, A338892.

Sequence in context: A085625 A116490 A230213 * A008607 A044077 A043350

Adjacent sequences: A338887 A338888 A338889 * A338891 A338892 A338893

Keyword

nonn

Author

Rémy Sigrist, Nov 14 2020

Status

approved