A120951 Numbers that are not the sum of 5 distinct nonzero squares.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 80, 81, 83, 84, 85, 86, 89, 91, 92, 93, 96, 97, 98, 101, 102, 104, 105, 107, 108, 109, 112, 113, 116, 117, 119, 122, 124, 125, 128, 133, 136, 137, 140, 141, 149, 153, 161, 164, 173, 177, 182, 188, 189, 197, 203, 221, 224, 236, 245

Offset

1,2

Comments

There are no other terms below 5000 and this list (of 124 terms) is probably complete. Is this known?

Thanks to R. K. Guy for supplying the references.

No others n < 10000. - T. D. Noe, Jul 23 2006

Bateman et al. prove that 245 is the last term. - T. D. Noe, Apr 03 2007

Links

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..124

Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, Sums of distinct squares, Acta Arithmetica 67 (1994), pp. 349-380.

E. Maitland Wright, The representation of a number as a sum of five or more squares, The Quarterly Journal of Mathematics, Volume os-4, Issue 1, 1933, Pages 37-51.

Index entries for sequences related to sums of squares

Mathematica

nn=300; t=Table[0, {nn}]; lim=Floor[Sqrt[nn]]; sq=Table[i^2, {i, lim}]; Do[n=sq[[i1]]+sq[[i2]]+sq[[i3]]+sq[[i4]]+sq[[i5]]; If[n<=nn, t[[n]]++ ], {i1, lim}, {i2, i1+1, lim}, {i3, i2+1, lim}, {i4, i3+1, lim}, {i5, i4+1, lim}]; Flatten[Position[t, 0]] (* T. D. Noe, Jul 23 2006 *)

Crossrefs

Cf. A004438.

Sequence in context: A247163 A376668 A357759 * A272554 A179797 A268200

Adjacent sequences: A120948 A120949 A120950 * A120952 A120953 A120954

Keyword

nonn,fini,full

Author

Franklin T. Adams-Watters, Jul 18 2006

Extensions

Entry revised by N. J. A. Sloane, Jul 23 2006

Status

approved