A001983 Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.

1, 4, 5, 9, 10, 13, 16, 17, 20, 25, 26, 29, 34, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 65, 68, 73, 74, 80, 81, 82, 85, 89, 90, 97, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 125, 130, 136, 137, 144, 145, 146, 148, 149, 153, 157, 160, 164

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

This sequence lists the values of A000404(n)/2 when A000404(n) is an even number. In other words, sequence lists integers n that are the average of two nonzero squares. - Altug Alkan, May 26 2016

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• G. Xiao, Two squares
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000404, subsequence of A001481, A004435 (complement), A025435, A004431.

Union of A000290 and A004431 excluding 0.

Programs

Haskell

a001983 n = a001983_list !! (n-1)
a001983_list = [x | x <- [0..], a025435 x > 0]
-- Reinhard Zumkeller, Dec 20 2013

Mathematica

upto=200;max=Floor[Sqrt[upto]];s=Total/@((Subsets[Range[0,max], {2}])^2);Union[Select[s,#<=upto&]]  (* Harvey P. Dale, Apr 01 2011 *)
selQ[n_] := Select[ PowersRepresentations[n, 2, 2], 0 <= #[[1]] < #[[2]] &] != {}; Select[Range[200], selQ] (* Jean-François Alcover, Oct 03 2013 *)

PARI

list(lim)=my(v=List()); for(x=0,sqrtint(lim\4), for(y=x+1, sqrtint(lim\1-x^2), listput(v, x^2+y^2))); Set(v) \\ Charles R Greathouse IV, Feb 07 2017

Formula

A025435(a(n)) > 0. - Reinhard Zumkeller, Dec 20 2013