A118905 Sum of legs of Pythagorean triangles (without multiple entries).

7, 14, 17, 21, 23, 28, 31, 34, 35, 41, 42, 46, 47, 49, 51, 56, 62, 63, 68, 69, 70, 71, 73, 77, 79, 82, 84, 85, 89, 91, 92, 93, 94, 97, 98, 102, 103, 105, 112, 113, 115, 119, 123, 124, 126, 127, 133, 136, 137, 138, 140, 141, 142, 146, 147, 151, 153, 154, 155, 158, 161, 164, 167, 168, 170, 175, 178, 182, 184, 186, 187, 188

Offset

1,1

Comments

The prime numbers in this sequence define A001132 (see comment in A001132). - Richard Choulet, Dec 16 2008

For the sum of legs of Pythagorean triangles with multiple entries see A198390. - Wolfdieter Lang, May 24 2013

Are these just the positive multiples of A001132? - Charles R Greathouse IV, May 28 2013

For the sum of legs of primitive Pythagorean triangles see A120681. - Wolfdieter Lang, Feb 17 2015

n is in the sequence iff A331671(n) > 0. - Ray Chandler, Feb 26 2020

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Example

7 = 3 + 4 and 3^2 + 4^2 = 5^2.
a(14) = 49 = 7^2 from the primitive Pythagorean triangle (x,y,z) = (9,40,41), and from the non-primitive one 7*(3,4,5); a(42) = 119 = 7*17 from four Pythagorean triangles (39,80,89) and (99,20,181) (both primitive) and 7*(5,12,13), 17*(3,4,5). - Wolfdieter Lang, May 24 2013

Prog

(PARI) is(n)=my(t=n^2); forstep(i=2-n%2, n-2, 2, if(issquare((t+i^2)/2), return(1))); 0 \\ Charles R Greathouse IV, May 28 2013
(Magma) [m:m in [2..200]|#[k:k in [1..m-1]|IsSquare(k^2+(m-k)^2)] ne 0]; // Marius A. Burtea, Jul 29 2019

Crossrefs

Cf. A009096, A118903, A118904, A058529, A001132, A120681, A331671.

Sequence in context: A100599 A353440 A198390 * A254064 A257224 A376046

Adjacent sequences: A118902 A118903 A118904 * A118906 A118907 A118908

Keyword

nonn

Author

Giovanni Resta, May 05 2006

Extensions

More terms from 147 on. - Richard Choulet, Nov 24 2009

Name specified. - Wolfdieter Lang, May 24 2013

Status

approved