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A261915
Smallest 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, 2, 3, 3, 2, 3, 3, -1, 4, 3, 3, 3, 4, 4, 3, -1, 4, 4, 4, 3, -1, 4, 5, -1, 4, 4, 4, 5, 4, 6, 5, -1, 6, 4, 5, 5, 6, 5, 6, -1, 4, 6, 5, 5, 6, 6, 5, -1, 6, 5, 7, 5, -1, 6, 6, -1, 8, 6, 5, 7, 6, 7, 6, -1, 6, 6, 7, 5, 6, 6, 7, -1, 8, 6, 8
OFFSET
0,5
COMMENTS
a(n) = -1 iff n is in A004215, a(n) >= 0 iff n is in A000378.
If we maximize x we get A261904.
EXAMPLE
Table 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 2 2 1
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 3 2 2
18 3 3 0
19 3 3 1
20 4 2 0
...
CROSSREFS
Analogs for 4 squares: A178786 and A122921.
Sequence in context: A083338 A241900 A204018 * A109037 A366136 A366693
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Sep 11 2015
EXTENSIONS
a(17) corrected, more terms from David Consiglio, Jr., Sep 11 2015
STATUS
approved