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

Author

David W. Wilson

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

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

Programs

Haskell

import Data.List (elemIndices)
a018825 n = a018825_list !! (n-1)
a018825_list = tail $ elemIndices 0 a025426_list
-- 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 *)

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

Formula

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