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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).
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
isA024364[an_] := Module[{r, s}, For[r = Floor[(an/4)^(1/2)], r <= Floor[(an/2)^(1/2)], r++, For[s = r - 1, s >= 1, s -= 2, If[2r(r + s) == an && GCD[r, s] < 2, Return[True]]; If[2r(r + s) < an, Break[]]]]; Return[False]];
Select[Range[2, 1000], isA024364] (* Jean-François Alcover, May 24 2024, after R. J. Mathar *)
CROSSREFS
Sequence in context: A307348 A289691 A145469 * A093507 A325802 A326019
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 13 10:09 EDT 2024. Contains 373383 sequences. (Running on oeis4.)