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Ordered set S defined by these rules: 0 and 2 are in S and if x is a nonzero number in S, then 2x-1 and 4x are in S.
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%I #18 Feb 18 2020 21:19:49

%S 0,2,3,5,8,9,12,15,17,20,23,29,32,33,36,39,45,48,57,60,63,65,68,71,77,

%T 80,89,92,95,113,116,119,125,128,129,132,135,141,144,153,156,159,177,

%U 180,183,189,192,225,228,231,237,240,249,252,255,257,260,263,269,272,281

%N Ordered set S defined by these rules: 0 and 2 are in S and if x is a nonzero number in S, then 2x-1 and 4x are in S.

%C The numbers 2 and 4x occupy the same positions in S that 1 occupies in the infinite Fibonacci word (A003849).

%H Ivan Neretin, <a href="/A060138/b060138.txt">Table of n, a(n) for n = 0..10000</a>

%H Clark Kimberling, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/goldentext.html">A Self-Generating Set and the Golden Mean</a>, J. Integer Sequences, 3 (2000), #00.2.8.

%H Clark Kimberling, <a href="https://www.fq.math.ca/Papers1/52-3/Kimberling11132013.pdf">Fusion, Fission, and Factors</a>, Fib. Q., 52 (2014), 195-202.

%Y Cf. A060142.

%K nonn

%O 0,2

%A _Clark Kimberling_, Mar 05 2001

%E Missing term a(55)=257 added by _Ivan Neretin_, Jun 19 2018