A024408 Perimeters of more than one primitive Pythagorean triangle.

1716, 2652, 3876, 3960, 4290, 5244, 5700, 5720, 6900, 6930, 8004, 8700, 9300, 9690, 10010, 10788, 11088, 12180, 12876, 12920, 13020, 13764, 14280, 15252, 15470, 15540, 15960, 16380, 17220, 17480, 18018, 18060, 18088, 18204, 19092, 19320, 20592, 20868

Offset

1,1

Comments

a(23) = 14280 is the first perimeter of 3 primitive Pythagorean triangles: {119, 7080, 7081}, {168, 7055, 7057} and {3255, 5032, 5993}. - Jean-François Alcover, Mar 14 2012

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Leon Bernstein, Primitive Pythagorean Triples, The Fibonacci Quarterly 20.3 (1982) 227-241.

Ron Knott, Pythagorean Triples and Online Calculators

Lindsay Witcosky, Perimeters of primitive Pythagorean triangles

Example

a(1) = 1716 with precisely two primitive Pythagorean triangles (with increasing entries): {195, 748, 773} and {364, 627, 725}. From Ron Knott's link. This is the first example of the family of perimeters 12*b(k)*(b(k) + 2) with b(k) = A007528(k), for k >= 2. See the Bernstein link, p. 234, Theorem 5. a). - Wolfdieter Lang, Sep 24 2019

Crossrefs

Cf. A007528, A024364, A103606.

Sequence in context: A157247 A347969 A267201 * A267741 A185795 A260474

Adjacent sequences: A024405 A024406 A024407 * A024409 A024410 A024411

Keyword

nonn

Author

David W. Wilson

Status

approved