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A024364 Ordered perimeters of primitive Pythagorean triangles. 21
12, 30, 40, 56, 70, 84, 90, 126, 132, 144, 154, 176, 182, 198, 208, 220, 234, 240, 260, 286, 306, 312, 330, 340, 374, 380, 390, 408, 418, 420, 442, 456, 462, 476, 494, 510, 532, 544, 546, 552, 570, 598, 608, 644, 646, 650, 672, 684, 690, 700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives perimeters A+B+C.

n is in this sequence iff A070109(n)>0. This is a subset of A010814.

For the corresponding primitive Pythagorean triples see A103606. - Wolfdieter Lang, Oct 06 2014

Any term in this sequence can be generated by f(m,n) = 2*m*(m+n), where m and n are positive coprime integers and m > 1, n < m, and m and n are not both odd. For example: f(2,1) = 2*2*(2+1) = 12. - Agola Kisira Odero, Apr 29 2016

LINKS

Table of n, a(n) for n=1..50.

Ron Knott, Pythagorean Triples and Online Calculators

FORMULA

a(n) = 2*A020886(n).

MAPLE

isA024364 := proc(an) local r::integer, s::integer ; for r from floor((an/4)^(1/2)) to floor((an/2)^(1/2)) do for s from r-1 to 1 by -2 do if 2*r*(r+s) = an and gcd(r, s) < 2 then RETURN(true) ; fi ; if 2*r*(r+s) < an then break ; fi ; od ; od : RETURN(false) ; end : for n from 2 to 400 do if isA024364(n) then printf("%d, ", n) ; fi ; od ; # R. J. Mathar, Jun 08 2006

MATHEMATICA

lst={}; amx=99; Do[For[b=a+1, b<(a^2/2), c=(a^2+b^2)^(1/2); If[c==IntegerPart[c]&&GCD[a, b, c]==1, p=a+b+c; AppendTo[lst, p]]; b=b+2], {a, 3, amx}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)

CROSSREFS

Cf. A020886.

Sequence in context: A083096 A289691 A145469 * A093507 A145470 A108278

Adjacent sequences:  A024361 A024362 A024363 * A024365 A024366 A024367

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 21 17:45 EDT 2017. Contains 290892 sequences.