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
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).
Programs
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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 -
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
Formula
a(n) = n + 124 for n > 121. - Charles R Greathouse IV, Jul 17 2011