|
%I #17 Apr 01 2014 10:34:10
%S 3,4,5,12,13,84,85,36,77,2964,2573,3925,1116,637,1285,893,924,43,925,
%T 372,997,497004,497005,138204,82597,161005,39973,155964,386827,417085,
%U 258037,327684,139763,356245,225924,82643,240565,37164,13573,39565,2388,39637,26412,11515,28813
%N Begin with a(0) = 3. Let a(n) for n > 0 be the smallest positive integer not yet in the sequence which forms part of a Primitive Pythagorean Triple (PPT) when paired with a(n-1).
%C I.e., the GCD of a(n) and a(n-1) is 1. That is why a(4)= 13 as opposed to A235598(4), which is 9.
%C Is the sequence infinite? Probably. But will it eventually contain all the terms of A042965 which are greater than 2? Probably not.
%H Robert G. Wilson v, <a href="/A239356/b239356.txt">Table of n, a(n) for n = 0..10000</a>
%t f[s_List] := Block[{n = s[[-1]]}, sol = Solve[ x^2 + y^2 == z^2 && GCD[x, y, z] == 1 && x > 0 && y > 0 && z > 0 && (x == n || z == n), {x, y, z}, Integers]; Append[s, Min[ Complement[ Union[ Extract[ sol, Position[ sol, _Integer]]], s]]]]; lst = Nest[f, {3}, 25]
%Y Cf. A235598.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Mar 16 2014
|
