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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

Sequence A024409 lists values of hypotenuse which are common to have more than one shape, and are all actually consisting of two shapes, except 1105 which is the first occurrence of 4 shapes. There are no occurrences of 3 shapes, or more than 4 in the range studied (hypotenuse values 5 to 10,000)

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..100

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). [From 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

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.