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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 (list; graph; refs; listen; history; text; internal format)
 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) Ron Knott, Pythagorean Triples and Online Calculators 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 Adjacent sequences: A024406 A024407 A024408 * A024410 A024411 A024412 KEYWORD nonn,changed AUTHOR David W. Wilson STATUS approved

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Last modified May 28 09:54 EDT 2023. Contains 362999 sequences. (Running on oeis4.)