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

Author

Franklin T. Adams-Watters, Jul 18 2006

Keywords

• nonn
• fini
• full

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

Crossrefs

Cf. A004438.

Programs

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 *)

Extensions

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