

A178786


Express n as the sum of four squares, x^2+y^2+z^2+w^2, with x>=y>=z>=w>=0, maximizing the value of x. Then a(n) is that x.


4



0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 8, 8, 7, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 9, 10
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OFFSET

0,5


COMMENTS

Lagrange's theorem tells us that each positive integer can be written as a sum of four squares.


LINKS

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


PROG

Python code :
from math import *
for nbre in range(0, 500): # or more than 500 !
....maxc4=0
....for c1 in range(0, sqrt(nbre/4)+1):
........for c2 in range(c1, sqrt(nbre/3)+1):
............for c3 in range(c2, sqrt(nbre/2)+1):
................s3=c3**2+c2**2+c1**2
................if s3<=nbre:
....................c4=sqrt(nbres3)
....................if int(c4)==c4 and c4>=c3:
........................if c4>maxc4:
............................maxc4=int(c4)
....print '%d, ' % maxc4,


CROSSREFS

Cf. A122922, A122923, A122924, A122925, A122926, A122927, A002330, A122921.
Analogs for 3 squares: A261904 and A261915.
Sequence in context: A227581 A263846 A350088 * A350174 A000196 A111850
Adjacent sequences: A178783 A178784 A178785 * A178787 A178788 A178789


KEYWORD

nonn


AUTHOR

Sébastien Dumortier, Jun 24 2011


STATUS

approved



