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%I #20 Jan 21 2020 13:20:20
%S 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 59,64,67,68,69,71,75,76,79,81,83,87,88,92,93,95,96,100,103,104,107,
%U 108,111,115,116,119,121,123,124,127,128,129,131,133,135,136,139,141,147
%N Numbers which form exclusively the shortest side of primitive Pythagorean triangles.
%C Union of A112398 and A112679.
%C 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 . . . . . . . . . 3
%C . . . . . . . . / ... \
%C . . . . . . . 4 ------- 5
%C . . . . . . . . . . . /...\
%C . . . . . . . . . . 12 -----13
%C . . . . . . . . . ./...\ .. /..\
%C . . . . . . . . . 35---37..84--85
%C - _Clark Kimberling_, Nov 14 2013
%H Ray Chandler, <a href="/A112680/b112680.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 nonn
%O 1,1
%A _Lekraj Beedassy_, Dec 30 2005
%E Corrected and extended by _Ray Chandler_, Jan 02 2006
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