A112398 -id:A112398 - cp's OEIS frontend

A112372 Odd legs of primitive Pythagorean triangles which are exclusively the short one.

3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 65, 67, 69, 71, 73, 75, 79, 81, 83, 85, 87, 89, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 145, 147, 149, 151

Offset: 1

Lekraj Beedassy, Dec 02 2005

nonn

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

Entries of A081874 (removing duplicates) excluding its subsequence A081934.

Cf. A112398.

Extended by Ray Chandler, Dec 08 2005

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

Original entry on oeis.org

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

Lekraj Beedassy, Dec 30 2005

nonn

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

Ray Chandler, Table of n, a(n) for n = 1..10000
Ron Knott, Generator of all Pythagorean triples that include a given number

Corrected and extended by Ray Chandler, Jan 02 2006

cp's OEIS Frontend

A112372 Odd legs of primitive Pythagorean triangles which are exclusively the short one.

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