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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").

%I A159781 #28 Dec 09 2019 13:21:06
%S A159781 1105,1885,2405,2465,2665,3145,3445,3485,3965,4505,4745,5185,5365,
%T A159781 5525,5785,5945,6205,6305,6409,6565,7085,7345,7565,7585,7685,8177,
%U A159781 8245,8585,8845,8905,9061,9265,9425,9605,9685,9805,10205,10585,10865
%N A159781 Values of hypotenuse of primitive Pythagorean triples which can have four different shapes (that is, four different sets of "legs").
%C A159781 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]
%C A159781 A024362(a(n)) = 4. - _Reinhard Zumkeller_, Dec 02 2012
%H A159781 Ray Chandler, <a href="/A159781/b159781.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Reinhard Zumkeller)
%t A159781 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 *)
%o A159781 (Haskell)
%o A159781 import Data.List (elemIndices)
%o A159781 a159781 n = a159781_list !! (n-1)
%o A159781 a159781_list = map (+ 1) $ elemIndices 4 a024362_list
%o A159781 -- _Reinhard Zumkeller_, Dec 02 2012
%Y A159781 Cf. A024409 and A146945.
%Y A159781 Cf. A006278 (8, 16, etc. shapes). - _R. J. Mathar_, Apr 12 2010
%K A159781 nonn
%O A159781 1,1
%A A159781 John T. Harrison (harrison_uk_2000(AT)yahoo.co.uk), Apr 22 2009
%E A159781 6429 replaced by 6409 and 3 terms added by _R. J. Mathar_, Apr 12 2010
%E A159781 Missing 8585 and 8845 inserted by _Reinhard Zumkeller_, Dec 02 2012