A159781 Values of hypotenuse of primitive Pythagorean triples which can have four different shapes (that is, four different sets of "legs").

1105, 1885, 2405, 2465, 2665, 3145, 3445, 3485, 3965, 4505, 4745, 5185, 5365, 5525, 5785, 5945, 6205, 6305, 6409, 6565, 7085, 7345, 7565, 7585, 7685, 8177, 8245, 8585, 8845, 8905, 9061, 9265, 9425, 9605, 9685, 9805, 10205, 10585, 10865

Offset

1,1

Comments

This is a subsequence of A024409, which lists hypotenuse values common to more than one primitive Pythagorean triple. A024409(1) = A006278(2) = 65 is the smallest hypotenuse common to exactly two primitive Pythagorean triples; a(1) = A006278(3) = 1105 is the smallest that is common to four. [edited by Jon E. Schoenfield, Aug 19 2018]

A024362(a(n)) = 4. - Reinhard Zumkeller, Dec 02 2012

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 100 terms from Reinhard Zumkeller)

Mathematica

f[c_] := f[c] = Block[{a = 1, b, cnt = 0, lmt = Floor[Sqrt[c^2/2]]}, While[b = Sqrt[c^2 - a^2]; a < lmt, If[IntegerQ@ b && GCD[a, b, c] == 1, cnt++]; a++]; cnt]Select[1 + 4 Range[2800], f@# > 2 &] (* Robert G. Wilson v, Mar 16 2014 *)

Prog

(Haskell)
import Data.List (elemIndices)
a159781 n = a159781_list !! (n-1)
a159781_list = map (+ 1) $ elemIndices 4 a024362_list
-- Reinhard Zumkeller, Dec 02 2012

Crossrefs

Cf. A024409 and A146945.

Cf. A006278 (8, 16, etc. shapes). - R. J. Mathar, Apr 12 2010

Sequence in context: A052155 A097102 A281877 * A264498 A102924 A214017

Adjacent sequences: A159778 A159779 A159780 * A159782 A159783 A159784

Keyword

nonn

Author

John T. Harrison (harrison_uk_2000(AT)yahoo.co.uk), Apr 22 2009

Extensions

6429 replaced by 6409 and 3 terms added by R. J. Mathar, Apr 12 2010

Missing 8585 and 8845 inserted by Reinhard Zumkeller, Dec 02 2012

Status

approved