

A159781


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 !! (n1)
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



