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A112680 Numbers which form exclusively the shortest side of primitive Pythagorean triangles. 1
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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A265350 A096315 A286395 * A096079 A298984 A094551
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Dec 30 2005
EXTENSIONS
Corrected and extended by Ray Chandler, Jan 02 2006
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)