A103253 Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and z is a perfect square.

7, 28, 41, 63, 112, 119, 161, 164, 175, 239, 252, 343, 369, 448, 476, 527, 567, 644, 656, 700, 721, 847, 956, 959, 1008, 1025, 1071, 1081, 1183, 1241, 1372, 1449, 1476, 1519, 1575, 1792, 1904, 2009, 2023, 2047, 2108, 2268, 2527, 2576, 2624, 2800, 2884, 2975

Offset

1,1

Comments

The case where x or y and z are squares does not occur.

Links

Table of n, a(n) for n=1..48.

MathForFun, Pythagorean triples

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

Example

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

Prog

(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]=y; print(x", "y", "z) ) ) ); vy=vector(c); w=vecsort(w); for(j=1, n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1, 200, print1(vy[j]", ") ) }

Crossrefs

Sequence in context: A267432 A155712 A015817 * A321777 A269451 A139607

Adjacent sequences: A103250 A103251 A103252 * A103254 A103255 A103256

Keyword

easy,nonn

Author

Cino Hilliard, Mar 20 2005

Status

approved