A004433 Numbers that are the sum of 4 distinct nonzero squares: of form w^2+x^2+y^2+z^2 with 0<w<x<y<z.

30, 39, 46, 50, 51, 54, 57, 62, 63, 65, 66, 70, 71, 74, 75, 78, 79, 81, 84, 85, 86, 87, 90, 91, 93, 94, 95, 98, 99, 102, 105, 106, 107, 109, 110, 111, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 129, 130, 131, 133, 134, 135, 137

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for sequences related to sums of squares

Formula

{n: A025443(n) >=1}. Union of A025386 and A025376. - R. J. Mathar, Jun 15 2018

Example

30 = 1^2+2^2+3^2+4^2.

Mathematica

data = Flatten[ DeleteCases[ FindInstance[ w^2 + x^2 + y^2 + z^2 == # && 0 < w < x < y < z < #, {w, x, y, z}, Integers] & /@ Range[137], {}], 1]; w^2 + x^2 + y^2 + z^2 /. data (* Ant King, Oct 17 2010 *)
Select[Union[Total[#^2]&/@Subsets[Range[10], {4}]], #<=137&] (* Harvey P. Dale, Jul 03 2011 *)

Prog

(Haskell)
a004433 n = a004433_list !! (n-1)
a004433_list = filter (p 4 $ tail a000290_list) [1..] where
   p k (q:qs) m = k == 0 && m == 0 ||
                  q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m)
-- Reinhard Zumkeller, Apr 22 2013
(PARI) list(lim)=my(v=List()); lim\=1; for(z=4, sqrtint(lim\4), for(y=3, min(sqrtint((lim-z^2)\3), z-1), for(x=2, min(sqrtint((lim-y^2-z^2)\2), y-1), for(w=1, min(sqrtint(lim-x^2-y^2-z^2), x-1), listput(v, w^2+x^2+y^2+z^2))))); Set(v) \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A001944, A001995, A003995, A004431, A004432, A004434, A224981, A224982, A224983, A000290.

Sequence in context: A325449 A243301 A001995 * A223727 A025376 A280640

Adjacent sequences: A004430 A004431 A004432 * A004434 A004435 A004436

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved