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A024409
Hypotenuses of more than one primitive Pythagorean triangle.
11
65, 85, 145, 185, 205, 221, 265, 305, 325, 365, 377, 425, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 725, 745, 785, 793, 845, 865, 901, 905, 925, 949, 965, 985, 1025, 1037, 1073, 1105, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1325
OFFSET
1,1
COMMENTS
The subsequence allowing 4 different shapes is in A159781. [R. J. Mathar, Apr 12 2010]
A024362(a(n)) > 1. - Reinhard Zumkeller, Dec 02 2012
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
EXAMPLE
65^2 = 16^2 + 63^2 = 33^2 + 56^2 (also = 25^2 + 60^2 = 39^2 + 52^2, but these are not primitive, with gcd = 5 resp. 13). Note that 65 = 1^2 + 8^2 = 4^2 + 7^2 is also the least integer > 1 to be a sum a^2 + b^2 with gcd(a,b) = 1 in two ways. - M. F. Hasler, May 18 2023
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@ 335, f@# > 1 &] (* Robert G. Wilson v, Mar 16 2014 *)
Select[Tally[Sqrt[Total[#^2]]&/@Union[Sort/@({Times@@#, (Last[#]^2-First[ #]^2)/2}&/@(Select[Subsets[Range[1, 71, 2], {2}], GCD@@# == 1&]))]], #[[2]]> 1&][[All, 1]]//Sort (* Harvey P. Dale, Sep 29 2018 *)
PROG
(Haskell)
import Data.List (findIndices)
a024409 n = a024409_list !! (n-1)
a024409_list = map (+ 1) $ findIndices (> 1) a024362_list
-- Reinhard Zumkeller, Dec 02 2012
CROSSREFS
Cf. A020882, A120960, subsequence of A008846.
Sequence in context: A084648 A224770 A274044 * A131574 A323272 A322781
KEYWORD
nonn
STATUS
approved