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A338890
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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PROG
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(C#) See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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