A004434 Numbers that are the sum of 5 distinct nonzero squares.

55, 66, 75, 79, 82, 87, 88, 90, 94, 95, 99, 100, 103, 106, 110, 111, 114, 115, 118, 120, 121, 123, 126, 127, 129, 130, 131, 132, 134, 135, 138, 139, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 162, 163

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, Sums of distinct squares, Acta Arithmetica 67 (1994), pp. 349-380.

Franz Halter-Koch, Darstellung natürlicher Zahlen als Summe von Quadraten, Acta Arithmetica 42 (1982), pp. 11-20.

Index entries for sequences related to sums of squares

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = n + 124 for n > 121. [Charles R Greathouse IV, Jul 17 2011]

Prog

(PARI) upto(lim)=my(v=List(), tb, tc, td, te); for(a=5, sqrt(lim), for(b=4, min(a-1, sqrt(lim-a^2)), tb=a^2+b^2; for(c=3, min(b-1, sqrt(lim-tb)), tc=tb+c^2; for(d=2, min(c-1, sqrt(lim-tc)), td=tc+d^2; for(e=1, d-1, te=td+e^2; if(te>lim, break, listput(v, te))))))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Jul 17 2011
(Haskell)
a004434 n = a004434_list !! (n-1)
a004434_list = filter (p 5 $ 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

Crossrefs

Cf. A003995, A004431, A004432, A004433, A224981, A224982, A224983, A000290.

Sequence in context: A043959 A285804 A269808 * A168109 A116055 A068898

Adjacent sequences: A004431 A004432 A004433 * A004435 A004436 A004437

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved