|
| |
|
|
A020882
|
|
Ordered hypotenuses (with multiplicity) of primitive Pythagorean triangles.
|
|
66
| |
|
|
5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 65, 73, 85, 85, 89, 97, 101, 109, 113, 125, 137, 145, 145, 149, 157, 169, 173, 181, 185, 185, 193, 197, 205, 205, 221, 221, 229, 233, 241, 257, 265, 265, 269, 277, 281, 289, 293, 305, 305, 313, 317, 325, 325, 337, 349, 353, 365, 365
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The largest member 'c' of the primitive Pythagorean triples (a,b,c) ordered by increasing c.
These are numbers of the form a^2+b^2 where gcd( b-a, 2*a*b)=1. [M. F. Hasler, Apr 04 2010]
a(n) = sqrt[{(A120681(n)^2 + A120682(n)^2}/2]. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 24 2006
Permutations are in A094194, A088511, A121727, A119321, A113482 and A081804. Entries of A024409 occur here more than once. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 12 2010]
|
|
|
LINKS
| M. F. Hasler, Table of n, a(n) for n = 1..1593
M. de Frenicle, Methode pour trouver la solutions des problems par les exclusions, in: Divers ouvrage des mathematique et de physique par messieurs de l'academie royale des science, (1693) pp 1-44.
Hans Isdahl, Pythagoras site (in Norwegian)
Ron Knott, Pythagorean Triples and Online Calculators
E. S. Rowland, Primitive Solutions to x^2 + y^2 = z^2
M. Somos, Table of primitive Pythagorean triplets and related parameters
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
|
FORMULA
| a(n) = sqrt(A046086(n)^2 + A046087(n)^2) [Zak Seidov, Apr 12 2011]
|
|
|
MATHEMATICA
| t={}; Do[Do[a=Sqrt[c^2-b^2]; If[a>b, Break[]]; If[IntegerQ[a]&&GCD[a, b, c]==1, AppendTo[t, c]], {b, c-1, 3, -1}], {c, 400}]; t (* From Vladimir Joseph Stephan Orlovsky, Jan 21 2012 *)
|
|
|
PROG
| (PARI) {my( c=0, new=[]); for( b=1, 99, for( a=1, b-1, gcd(b-a, 2*a*b) == 1 && new=concat(new, a^2+b^2)); new=vecsort(new); for( j=1, #new, new[j] > (b+1)^2 & (new=vecextract(new, Str(j, ".."))) & next(2); write("b020882.txt", c++, " "new[j])); new=[])} (M. F. Hasler, Apr 04 2010)
|
|
|
CROSSREFS
| Cf. A004613, A008846, A020883-A020886, A046086, A046087, A134961.
Sequence in context: A037046 A126887 A087445 * A081804 A004613 A008846
Adjacent sequences: A020879 A020880 A020881 * A020883 A020884 A020885
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane, May 15 2010
|
| |
|
|
