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A024364 Ordered perimeters of primitive Pythagorean triangles. 30
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, 714, 736, 756 (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.

k is in this sequence iff A070109(k) > 0. This is a subsequence 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,k) = 2*m*(m+k), where m and k are positive coprime integers and m > 1, k < m, and m and k are not both odd. For example: f(2,1) = 2*2*(2+1) = 12. - Agola Kisira Odero, Apr 29 2016

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000 (duplicates removed by Sean A. Irvine)

Leon Bernstein, On primitive Pythagorean triangles with equal perimeters, The Fibonacci Quarterly 27.1 (1989) 2-6 (and the earlier Bernstein paper 20.3 (1982) 227-241, see A024408).

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, A024408.

Sequence in context: A307348 A289691 A145469 * A093507 A325802 A326019

Adjacent sequences:  A024361 A024362 A024363 * A024365 A024366 A024367

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 28 13:05 EDT 2022. Contains 354115 sequences. (Running on oeis4.)