A112680 Numbers which form exclusively the shortest side of primitive Pythagorean triangles.

3, 7, 8, 9, 11, 16, 19, 20, 23, 27, 28, 31, 32, 33, 36, 39, 43, 44, 47, 48, 49, 51, 52, 57, 59, 64, 67, 68, 69, 71, 75, 76, 79, 81, 83, 87, 88, 92, 93, 95, 96, 100, 103, 104, 107, 108, 111, 115, 116, 119, 121, 123, 124, 127, 128, 129, 131, 133, 135, 136, 139, 141, 147

Offset

1,1

Comments

Union of A112398 and A112679.

Let S consist of integers x such that x is a term of a primitive Pythagorean triple (ppt). Consider the equivalence classes induced on S by this relation: x and y are equivalent if some ppt includes both x and y. For each class E, let x(E) be the least number in E. Then (a(n)) is the result of arranging the numbers x(E) in increasing order. The terms of S can be represented as nodes of a disconnected graph whose components match the classes C. For example, the component represented by a(1) = 3 starts with

. . . . . . . . . 3

. . . . . . . . / ... \

. . . . . . . 4 ------- 5

. . . . . . . . . . . /...\

. . . . . . . . . . 12 -----13

. . . . . . . . . ./...\ .. /..\

. . . . . . . . . 35---37..84--85

- Clark Kimberling, Nov 14 2013

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Ron Knott, Generator of all Pythagorean triples that include a given number

Crossrefs

Sequence in context: A265350 A096315 A286395 * A096079 A298984 A094551

Adjacent sequences: A112677 A112678 A112679 * A112681 A112682 A112683

Keyword

nonn

Author

Lekraj Beedassy, Dec 30 2005

Extensions

Corrected and extended by Ray Chandler, Jan 02 2006

Status

approved