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A088976 Breadth-first traversal of the Collatz tree, with the even child of each node traversed prior to its odd child. If the Collatz 3n+1 conjecture is true, this is a permutation of all positive integers.

%I A088976 #13 Jul 21 2021 09:06:14
%S A088976 1,2,4,8,16,32,5,64,10,128,21,20,3,256,42,40,6,512,85,84,80,13,12,
%T A088976 1024,170,168,160,26,24,2048,341,340,336,320,53,52,48,4096,682,680,
%U A088976 113,672,640,106,104,17,96,8192,1365,1364,227,1360,226,1344,1280,213,212,35,208
%N A088976 Breadth-first traversal of the Collatz tree, with the even child of each node traversed prior to its odd child. If the Collatz 3n+1 conjecture is true, this is a permutation of all positive integers.
%H A088976 T. D. Noe, <a href="/A088976/b088976.txt">Table of n, a(n) for n = 0..3517</a>
%o A088976 (Python)
%o A088976 def A088976():
%o A088976     yield 1
%o A088976     for x in A088976():
%o A088976         yield 2*x
%o A088976         if x > 4 and x % 6 == 4:
%o A088976             yield (x - 1)//3
%o A088976 a = A088976(); print([next(a) for _ in range(100)])
%Y A088976 Cf. A127824 (terms at the same depth are sorted).
%K A088976 easy,nonn
%O A088976 0,2
%A A088976 _David Eppstein_, Oct 31 2003