cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A112680 #20 Jan 21 2020 13:20:20
%S A112680 3,7,8,9,11,16,19,20,23,27,28,31,32,33,36,39,43,44,47,48,49,51,52,57,
%T A112680 59,64,67,68,69,71,75,76,79,81,83,87,88,92,93,95,96,100,103,104,107,
%U A112680 108,111,115,116,119,121,123,124,127,128,129,131,133,135,136,139,141,147
%N A112680 Numbers which form exclusively the shortest side of primitive Pythagorean triangles.
%C A112680 Union of A112398 and A112679.
%C A112680 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
%C A112680 . . . . . . . . . 3
%C A112680 . . . . . . . . / ... \
%C A112680 . . . . . . . 4 ------- 5
%C A112680 . . . . . . . . . . . /...\
%C A112680 . . . . . . . . . . 12 -----13
%C A112680 . . . . . . . . . ./...\ .. /..\
%C A112680 . . . . . . . . . 35---37..84--85
%C A112680   - _Clark Kimberling_, Nov 14 2013
%H A112680 Ray Chandler, <a href="/A112680/b112680.txt">Table of n, a(n) for n = 1..10000</a>
%H A112680 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html#moregen">Generator of all Pythagorean triples that include a given number</a>
%K A112680 nonn
%O A112680 1,1
%A A112680 _Lekraj Beedassy_, Dec 30 2005
%E A112680 Corrected and extended by _Ray Chandler_, Jan 02 2006