A018825 Numbers that are not the sum of 2 nonzero squares.

1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 16, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 36, 38, 39, 42, 43, 44, 46, 47, 48, 49, 51, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 75, 76, 77, 78, 79, 81, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

Formula

A025426(a(n)) = 0; A063725(a(n)) = 0. - Reinhard Zumkeller, Aug 16 2011

Maple

isA000404 := proc(n)
    local x, y ;
    for x from 1 do
        if x^2> n then
            return false;
        end if;
        for y from 1 do
            if x^2+y^2 > n then
                break;
            elif x^2+y^2 = n then
                return true;
            end if;
        end do:
    end do:
end proc:
A018825 := proc(n)
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if not isA000404(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A018825(n), n=1..30) ; # R. J. Mathar, Jul 28 2014

Mathematica

q=13; q2=q^2+1; lst={}; Do[Do[z=a^2+b^2; If[z<=q2, AppendTo[lst, z]], {b, a, 1, -1}], {a, q}]; lst; u=Union@lst; Complement[Range[q^2], u] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)

Prog

(Haskell)
import Data.List (elemIndices)
a018825 n = a018825_list !! (n-1)
a018825_list = tail $ elemIndices 0 a025426_list
-- Reinhard Zumkeller, Aug 16 2011
(PARI) is(n)=my(f=factor(n), t=prod(i=1, #f~, if(f[i, 1]%4==1, f[i, 2]+1, if(f[i, 2]%2 && f[i, 1]>2, 0, 1)))); if(t!=1, return(!t)); for(k=sqrtint((n-1)\2)+1, sqrtint(n-1), if(issquare(n-k^2), return(0))); 1 \\ Charles R Greathouse IV, Sep 02 2015

Crossrefs

Cf. A022544, A081324, A000404 (complement), A004431.

Sequence in context: A065313 A103566 A258592 * A247779 A243989 A248521

Adjacent sequences: A018822 A018823 A018824 * A018826 A018827 A018828

Keyword

nonn

Author

David W. Wilson

Status

approved