login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248943 Sum of squares of diagonals of a parallelogram (but not rectangle or rhombus) with integer sides and diagonals and their GCD is 1. 0

%I

%S 130,170,250,260,290,340,370,410,442,500,530,580,610,650,650,650,730,

%T 740,754,820,850,850,850,884,890,962,970,986,1010,1060,1066,1090,1130,

%U 1220,1250,1258,1300,1300,1300,1370,1378,1394,1450,1450,1450,1460,1490,1508,1570,1586,1690,1690,1690,1700,1700,1700,1730

%N Sum of squares of diagonals of a parallelogram (but not rectangle or rhombus) with integer sides and diagonals and their GCD is 1.

%C Alternate definition: Lists of P satisfying P = 2a^2 + 2b^2 = c^2 + d^2 (by parallelogram law) and a + b > max(c,d) (by triangle inequality) and a!=b (removes rhombus) and c!=d (removes rectangle) and gcd(a,b,c,d)=1.

%e a...b...c...d...P=2a^2+2b^2=c^2+d^2

%e 4...7...7...9...130

%e 6...7...7...11..170

%e 5...10..9...13..250

%e 7...9...8...14..260

%e 8...9...11..13..290

%e 7...11..12..14..340

%e 8...11..9...17..370

%e 6...13..11..17..410

%e 10..11..9...19..442

%e 9...13..10..20..500

%t PMax=2000;

%t Do[Sqrt[P/2-a^2]//If[IntegerQ[#]&&GCD[a,#,c[[1]],c[[2]]]==1,P//Sow]&,{P,2,PMax,2},{c,DeleteCases[PowersRepresentations[P,2,2],{x_,x_}]},{a,(c[[2]]-c[[1]])/2+1,Sqrt[P]/2-1//Ceiling}]//Reap//Last//Last

%K nonn

%O 1,1

%A _Albert Lau_, Oct 17 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 2 01:30 EDT 2022. Contains 357191 sequences. (Running on oeis4.)