A122926 -id:A122926 - cp's OEIS frontend

A122921 Express n as the sum of four squares, x^2+y^2+z^2+w^2, x>=y>=z>=w>=0, minimizing the value of x. a(n) is that x.

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 4, 4, 3, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4, 4, 4, 5, 4, 5, 5, 4, 4, 4, 5, 4, 6, 5, 5, 6, 4, 5, 5, 5, 5, 6, 5, 4, 6, 5, 5, 5, 6, 5, 6, 6, 5, 6, 5, 5, 6, 6, 5, 6, 6, 5, 7, 5, 6, 6, 6, 6, 6, 6, 5, 6, 6, 7, 6, 8, 6, 6, 7, 5, 6, 6, 7, 6

Offset: 0

Franklin T. Adams-Watters, Sep 19 2006

nonn

			10 = 2^2 + 2^2 + 1^2 + 1^2, so a(10) = 2. The only representation for 11 is 3^2 + 1^2 + 1^2 + 0^2, so a(11) = 3.

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

Cf. A122922, A122923, A122924, A122925, A122926, A122927, A002330.

Analogs for 3 squares: A261904 and A261915.

A122927 Number of occurrences of n in A122921.

Original entry on oeis.org

1, 4, 9, 15, 21, 24, 37, 38, 48, 50, 61, 62, 81, 75, 87, 93, 109, 99, 123, 109, 138, 132, 149, 133, 178, 154, 179, 171, 198, 179, 215, 196, 233, 211, 238, 221, 268, 236, 268, 246, 299, 269, 302, 282, 323, 295, 327, 305, 374, 322, 355, 337, 396, 339, 402, 358

Offset: 0

Franklin T. Adams-Watters, Sep 19 2006

nonn

The first such occurrence is at A122925(n); the last is at 4n^2.

Cf. A122921, A122925, A122926.

A122925 Index of first occurrence of n in A122921.

Original entry on oeis.org

0, 1, 5, 11, 24, 39, 53, 83, 96, 155, 176, 257, 224, 335, 376, 499, 384, 687, 701, 899, 704, 1043, 1104, 1379, 896, 1559, 1584, 1883, 1504, 2239, 2096, 2617, 1536, 2963, 2864, 3259, 2912, 3761, 3728, 3956, 2816, 4529, 4304, 5276, 4416, 5588, 5688, 5849

Offset: 0

Franklin T. Adams-Watters, Sep 19 2006

nonn

The last occurrence of n in A122921 is at 4n^2.

Cf. A122921, A122926, A122927.

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.

Original entry on oeis.org

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

Offset: 0

Sébastien Dumortier, Jun 24 2011

nonn

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

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

Cf. A122922, A122923, A122924, A122925, A122926, A122927, A002330, A122921.

Analogs for 3 squares: A261904 and A261915.

from math import *
for nbre in range(0, 500): # or more than 500 !
    maxc4=0
    for c1 in range(0, int(sqrt(nbre/4))+1):
        for c2 in range(c1, int(sqrt(nbre/3))+1):
            for c3 in range(c2, int(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(maxc4, end=', ')

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A122921 Express n as the sum of four squares, x^2+y^2+z^2+w^2, x>=y>=z>=w>=0, minimizing the value of x. a(n) is that x.

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A122927 Number of occurrences of n in A122921.

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A122925 Index of first occurrence of n in A122921.

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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.

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