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 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 (list; graph; refs; listen; history; text; internal format)
 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(nbre-s3) ....................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

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Last modified November 26 07:57 EST 2022. Contains 358354 sequences. (Running on oeis4.)