A261904 - OEIS

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.

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

David Consiglio, Jr., Table of n, a(n) for n = 0..10000

David Consiglio, Jr., Python Program

Index entries for sequences related to sums of squares

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

Cf. A000378, A004215, A005875, A261915.

Analogs for 4 squares: A178786 and A122921.

Sequence in context: A262982 A205011 A130790 * A297030 A266348 A179647

Adjacent sequences: A261901 A261902 A261903 * A261905 A261906 A261907

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Sep 08 2015

EXTENSIONS

More terms from David Consiglio, Jr., Sep 08 2015

STATUS

approved