A365577 Sequence of the short legs of primitive Pythagorean triples beginning with the triple (3,4,5), with each subsequent triple having as its short leg the sum of the legs of the previous triple, and with the long leg and the hypotenuse of each triple being consecutive natural numbers.
3, 7, 31, 511, 131071, 8589934591, 36893488147419103231, 680564733841876926926749214863536422911, 231584178474632390847141970017375815706539969331281128078915168015826259279871
Offset: 1
Keywords
Examples
Triangles begin: 3, 4, 5; 7, 24, 25; 31, 480, 481; 511, 130560, 130561; ... This sequence is the first column.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..11
- Miguel-Ángel Pérez García-Ortega, Capitulo 5. Catetos, El Libro de las Ternas Pitagóricas.
Formula
(a_1, b_1, c_1) = (3,4,5) and for each n > 1:
(a_n, b_n, c_n) = (a_(n-1)+b_(n-1), ((a_(n-1)+b_(n-1))^2-1)/2, ((a_(n-1)+b_(n-1))^2+1)/2)
Comments