|
Search: id:A120090
|
|
|
| A120090 |
|
Numbers whose square is the perimeter of a primitive Pythagorean triangle. |
|
+0
3
|
|
| 12, 30, 56, 90, 132, 154, 182, 208, 234, 240, 306, 340, 374, 380, 408, 418, 456, 462, 494, 546, 552, 598, 644, 650, 690, 700, 736, 756, 800, 850, 864, 870, 918, 928, 986, 992, 1026, 1044, 1054, 1102, 1116, 1122, 1160, 1178, 1240, 1254, 1260, 1302, 1320
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
a(n)=sqrt(A120089).
|
|
LINKS
|
P. Yiu, "Primitive Pythagorean triangles with square perimeters" in 'Recreational Mathematics' Chap.6.2 pp. 50/360
|
|
FORMULA
|
a(n)=2*u*v, where u=sqrt(j/2) and v=sqrt(j+k) {for coprime pairs(j,k) j>k with odd k such that pairs (u,v) are coprime with v odd}.
|
|
MAPLE
|
isA024364 := proc(an) local r::integer, s::integer ; for r from floor((an/4)^(1/2)) to floor((an/2)^(1/2)) do for s from r-1 to 1 by -2 do if 2*r*(r+s) = an and gcd(r, s) < 2 then RETURN(true) ; fi ; if 2*r*(r+s) < an then break ; fi ; od ; od : RETURN(false) ; end : for n from 2 to 1200 do if isA024364(n^2) then printf("%d, ", n) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
|
|
CROSSREFS
|
Sequence in context: A131874 A111396 A080385 this_sequence A086830 A084699 A064483
Adjacent sequences: A120087 A120088 A120089 this_sequence A120091 A120092 A120093
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 07 2006
|
|
EXTENSIONS
|
Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
|
|
|
Search completed in 0.002 seconds
|
