A103250 Numbers x, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and y is a perfect square.

30, 40, 120, 130, 160, 270, 272, 312, 350, 360, 480, 510, 520, 640, 738, 750, 888, 1000, 1080, 1088, 1160, 1170, 1200, 1218, 1248, 1342, 1400, 1440, 1470, 1920, 1960, 2040, 2080, 2080, 2210, 2430, 2448, 2560, 2590, 2808, 2952, 2968, 3000, 3150, 3240, 3250

Offset

1,1

Comments

The case where x and y are both squares cannot occur.

Links

Table of n, a(n) for n=1..46.

MathForFun, Pythagorean triples

Chenglong Zou, Peter Otzen, Cino Hilliard, Pythagorean triplets, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.

Example

x=30, y=16, 30^2 + 16^2 = 34^2. 30 is the 1st entry in the list.

Prog

(PARI) pythtrisq(n) = { local(a, b, c=0, k, x, y, z, vy, wx, vx, 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(y), 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]", ") ) }

Crossrefs

Sequence in context: A280640 A152616 A309306 * A181638 A166650 A275193

Adjacent sequences: A103247 A103248 A103249 * A103251 A103252 A103253

Keyword

easy,nonn

Author

Cino Hilliard, Mar 19 2005

Status

approved