Re: Integers that are the sum of 2 nonzero squares in exactly 2 ways

*To*: mathgroup at smc.vnet.net*Subject*: [mg125702] Re: Integers that are the sum of 2 nonzero squares in exactly 2 ways*From*: Dana DeLouis <dana01 at me.com>*Date*: Thu, 29 Mar 2012 03:02:03 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> the sum of 2 nonzero squares in exactly 2 ways. The smallest example is 50 Hi. The number 50 actually has 12 if you include negative numbers. :>o SquaresR[2,50] 12 Plus@@({-5,+5}^2) 50 Plus@@({-7,-1}^2) 50 etc... > I get a more or less straight line with a slope of about 8.85. Not sure, but the first 3 seems to have a slope of about 17. t=Table[{n,PowersRepresentations[n,2,2]},{n,86}]; tt=First/@Select[t,Length[Last[#]]==2 &] //Rest {50,65,85} FindFit[tt,a *x +b,{a,b},x] //Expand {a->17.5,b->31.6667} If we search the first 100,000 numbers, then the slope drops down to 11.8 Just curious... how many numbers did you go out? t=Table[{n,PowersRepresentations[n,2,2]},{n,100000}]; tt=First/@Select[t,Length[Last[#]]==2 &] //Rest; FindFit[tt,a *x +b,{a,b},x] //Expand {a->11.8312,b->102.192} Using Differences returns about the same number as slope: tt//Differences//Mean//N 11.8238 = = = = = = = = = = HTH :>) Dana DeLouis Mac & Math 8 = = = = = = = = = = On Mar 28, 6:00 am, Cisco Lane <travl... at yahoo.com> wrote: > I've been looking at integers that are the sum of 2 nonzero squares in exactly 2 ways. The smallest example is 50 = 5^2+5^2=7^2+1^2. The first few terms are 50, 65, 85, 125, 130, 145, .... This is given in OEIS ashttps://oeis.org/A025285 > > If I plot the pairs {1,50},{2,65},{3,85},... I get a more or less straight line with a slope of about 8.85... In other words, eventually, about one in 8.85 integers qualify. > > I wonder if there is a theoretical value for this approximate number of 8.85...?