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!)
A103251 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square. 2

%I #20 Nov 14 2019 17:56:46

%S 24,96,120,216,240,336,384,480,600,720,840,840,864,960,1080,1176,1320,

%T 1344,1536,1920,1944,2016,2160,2184,2400,2520,2880,2904,3000,3024,

%U 3360,3360,3360,3456,3696,3840,3960,4056,4320,4704,4896,5280,5280,5376,5400

%N Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.

%C There exists no case in which x or y and z are squares.

%C Also area A of the right triangles such that A, the sides and the circumradius are integers. - _Michel Lagneau_, Mar 15 2012

%H MathForFun, <a href="http://groups.yahoo.com/group/mathforfun/message/9962">Pythagorean triples</a>

%H Chenglong Zou, Peter Otzen, Cino Hilliard, <a href="/A103246/a103246.txt">Pythagorean triplets</a>, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.

%e x=24, y=7, 24^2 + 7^2 = 25^2. 24 is the 1st entry in the list.

%o (PARI) pythtrisq(n) = { local(a,b,c=0,k,x,y,z,vy,wx,vx,vz,j); w = vector(n*n+1); for(a=1,n, for(b=1,n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(z), c++; w[c]=x; print(x","y","z) ) ) ); vx=vector(c); w=vecsort(w); for(j=1,n*n, if(w[j]>0, k++; vx[k]=w[j]; ) ); for(j=1,200, print1(vx[j]",") ) }

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Mar 20 2005

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 March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)