

A063954


Every number is the sum of 4 squares; these are the odd numbers such that the first square can be taken to be any square < n.


5



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
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OFFSET

1,2


COMMENTS

This sequence is finite, with 52 terms.
This is a variant of A063951 where the arbitrary first squares must be positive. This makes a difference only for n = 7 and n = 15, which are in A063951 but not in this sequence, because for these two n and k = 0, n  k^2 is in A004215, i.e., not the sum of fewer than 4 squares.  M. F. Hasler, Jan 27 2018


REFERENCES

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


LINKS

Table of n, a(n) for n=1..52.
Gordon Pall, On Sums of Two or Four Values of a Quadratic Function of x, Transactions of the American Mathematical Society, Vol. 34, No. 1, (January 1932), pp. 98125.  Ant King, Nov 01 2010


MATHEMATICA

j[k_] := If[Union[Flatten[PowersRepresentations[k, 4, 2]]^2] == (#^2&/@Range[0, Sqrt[k]]), True, False]; Select[Range[1, 1250, 2], j] [From Ant King, Nov 01 2010]


PROG

(PARI) is_A063954(n)=bittest(n, 0)&&!forstep(k=sqrtint(n1), 0, 1, isA004215(nk^2)&&return) \\ M. F. Hasler, Jan 27 2018


CROSSREFS

Cf. A063949, A063950, A063951, A063952, A063953.
Sequence in context: A076052 A050556 A138008 * A123509 A196094 A063915
Adjacent sequences: A063951 A063952 A063953 * A063955 A063956 A063957


KEYWORD

nonn,easy,nice,fini,full


AUTHOR

N. J. A. Sloane, Sep 04 2001


STATUS

approved



