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
KEYWORD
nonn
AUTHOR
STATUS
approved