This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063954 #25 Aug 11 2025 10:21:33 %S A063954 1,3,5,9,13,17,21,25,33,41,45,49,57,65,73,81,89,97,105,129,145,153, %T A063954 169,177,185,201,209,217,225,257,273,297,305,313,329,345,353,385,425, %U A063954 433,441,481,513,561,585,609,689,697,713,817,825,945 %N 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. %C A063954 This sequence is finite, with 52 terms. %C A063954 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 %D A063954 J. H. Conway, personal communication, Aug 27, 2001. %H A063954 Gordon Pall, <a href="https://doi.org/10.1090/S0002-9947-1932-1501631-X">On Sums of Two or Four Values of a Quadratic Function of x</a>, Transactions of the American Mathematical Society, Vol. 34, No. 1, (January 1932), pp. 98-125. - _Ant King_, Nov 01 2010 %t A063954 j[k_] := If[Union[Flatten[PowersRepresentations[k,4,2]]^2] == (#^2&/@Range[0,Sqrt[k]]), True, False]; Select[Range[1,1250,2], j] (* _Ant King_, Nov 01 2010 *) %o A063954 (PARI) is_A063954(n)=bittest(n, 0)&&!forstep(k=sqrtint(n-1), 0, -1, isA004215(n-k^2)&&return) \\ _M. F. Hasler_, Jan 27 2018 %Y A063954 Cf. A063949, A063950, A063951, A063952, A063953. %K A063954 nonn,easy,nice,fini,full %O A063954 1,2 %A A063954 _N. J. A. Sloane_, Sep 04 2001