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A261904
Largest x such that n can be written as n = x^2 + y^2 + z^2 with x >= y >= z >= 0, or -1 if no such x exists.
4
0, 1, 1, 1, 2, 2, 2, -1, 2, 3, 3, 3, 2, 3, 3, -1, 4, 4, 4, 3, 4, 4, 3, -1, 4, 5, 5, 5, -1, 5, 5, -1, 4, 5, 5, 5, 6, 6, 6, -1, 6, 6, 5, 5, 6, 6, 6, -1, 4, 7, 7, 7, 6, 7, 7, -1, 6, 7, 7, 7, -1, 6, 7, -1, 8, 8, 8, 7, 8, 8, 6, -1, 8, 8, 8, 7, 6, 8, 7, -1, 8, 9, 9
OFFSET
0,5
COMMENTS
a(n) = -1 iff n is in A004215, a(n) >= 0 iff n is in A000378.
Somehow maximizing x seems like the right thing to do (since it is natural to try a greedy algorithm first). If we minimize x we get A261915.
EXAMPLE
Tabls showing initial values of n,x,y,z:
0 0 0 0
1 1 0 0
2 1 1 0
3 1 1 1
4 2 0 0
5 2 1 0
6 2 1 1
7 -1 -1 -1
8 2 2 0
9 3 0 0
10 3 1 0
11 3 1 1
12 2 2 2
13 3 2 0
14 3 2 1
15 -1 -1 -1
16 4 0 0
17 4 1 0
18 4 1 1
19 3 3 1
20 4 2 0
...
CROSSREFS
Analogs for 4 squares: A178786 and A122921.
Sequence in context: A262982 A205011 A130790 * A297030 A266348 A179647
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Sep 08 2015
EXTENSIONS
More terms from David Consiglio, Jr., Sep 08 2015
STATUS
approved