|
Search: id:A164282
|
|
|
| A164282 |
|
Hypotenuses of more than 2 Pythagorean triangle. |
|
+0
2
|
|
| 65, 85, 125, 130, 145, 170, 185, 195, 205, 221, 250, 255, 260, 265, 290, 305, 325, 340, 365, 370, 375, 377, 390, 410, 425, 435, 442, 445, 455, 481, 485, 493, 500, 505, 510, 520, 530, 533, 545, 555, 565, 580, 585, 595
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Also, hypotenuses of pythagorean triangle in pythagorean triples (a,b,c, a<b<c) such that a and b are the hypotenuse of pythagorean triangle, where the pythagorean triples (x1,y1,a) and (x2,y2,b) are similar triangle. But the pythagorean triples (a,b,c) and (x1,y1,a) are not similar. sequence gives c values. -Naohiro Nomoto
65^2 = 63^2 + 16^2 = 60^2 + 25^2 = 56^2 + 33^2 = 52^2 + 39^2
|
|
EXAMPLE
|
e.g. (a=25, b=60, c=65, a^2+b^2=c^2) ; 25 and 60 are the hypotenuse of pythagorean triangle. The pythagorean triples (15, 20, 25) and (36, 48, 60) are similar triangle. But the pythagorean triples (25, 60, 65) and (15, 20, 25) are not similar. So c=65 is in the sequence. -Naohiro Nomoto
e.g. (a=39, b=52, c=65, a^2+b^2=c^2) ; 39 and 52 are the hypotenuse of pythagorean triangle. The pythagorean triples (15, 36, 39) and (20, 48, 52) are similar triangle. But the pythagorean triples (39, 52, 65) and (15, 36, 39) are not similar. So c=65 is in the sequence. -Naohiro Nomoto
|
|
MATHEMATICA
|
Clear[lst, f, n, i, k] f[n_]:=Module[{i=0, k=0}, Do[If[Sqrt[n^2-i^2]==IntegerPart[Sqrt[n^2-i^2]], k++ ], {i, n-1, 1, -1}]; k/2]; lst={}; Do[If[f[n]>2, AppendTo[lst, n]], {n, 5*5!}]; lst
|
|
CROSSREFS
|
Cf. A009177, A084646, A084647, A084648, A084649
Sequence in context: A113688 A159758 A056693 this_sequence A025312 A024508 A025303
Adjacent sequences: A164279 A164280 A164281 this_sequence A164283 A164284 A164285
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 12 2009
|
|
|
Search completed in 0.002 seconds
|
