A063952 Of course every number is the sum of 4 squares; for these numbers the first square can be taken to be any square < n.

0, 1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 14, 17, 18, 20, 21, 22, 25, 26, 30, 33, 34, 36, 38, 41, 42, 45, 46, 49, 50, 52, 54, 57, 58, 62, 65, 66, 68, 70, 73, 74, 78, 81, 82, 84, 86, 89, 90, 94, 97, 98, 100, 102, 105, 106, 110, 114, 118, 122, 126, 129, 130, 132, 134

Offset: 1

Author

N. J. A. Sloane, Sep 04 2001

Keywords

• nonn
• easy
• nice

References

• J. H. Conway, personal communication, Aug 27, 2001.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1105 (numbers < 4000)

Crossrefs

Cf. A063949-A063954.

Programs

Mathematica

t1 = {1, 3, 5, 9, 13, 17, 21, 25, 33, 41, 45, 49, 57, 65, 73, 81, 89, 97, 105, 129, 145, 153, 169, 177, 185, 201, 209, 217, 225, 257, 273, 297, 305, 313, 329, 345, 353, 385, 425, 433, 441, 481, 513, 561, 585, 609, 689, 697, 713, 817, 825, 945}; t = Union[{0}, t1, 4*t1, 4*Range[0,999] + 2] (* T. D. Noe, Feb 22 2012 *)

Formula

Consists of 0, the 52 odd numbers in A063954, 4 times those numbers and all numbers of the form 4m+2.