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%I #23 Apr 27 2020 08:16:44
%S 0,2,1,5,6,3,4,12,13,14,16,17,7,8,9,34,10,11,30,31,32,35,36,33,37,41,
%T 42,43,45,46,18,19,20,23,15,21,22,24,88,89,92,25,26,27,81,28,29,77,78,
%U 79,82,83,80,84,90,93,91,94,106,85,86,95,96,87,97,107,108
%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n and a(n) have no common 1 in their base phi representations.
%C This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A330984/b330984.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A330984/a330984.png">Scatterplot of (x, y) such that x and y have no common 1 in their base phi representations and 0 <= x, y <= 1000</a>
%H Rémy Sigrist, <a href="/A330984/a330984.gp.txt">PARI program for A330984</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside the base phi representations of n and of a(n), are:
%e n a(n) phi(n) phi(a(n))
%e -- ---- ---------- -------------
%e 0 0 0 0
%e 1 2 1 10.01
%e 2 1 10.01 1
%e 3 5 100.01 1000.1001
%e 4 6 101.01 1010.0001
%e 5 3 1000.1001 100.01
%e 6 4 1010.0001 101.01
%e 7 12 10000.0001 100000.101001
%e 8 13 10001.0001 100010.001001
%e 9 14 10010.0101 100100.001001
%e 10 16 10100.0101 101000.100001
%o (PARI) See Links section.
%Y Cf. A238757 (binary analog), A331212.
%K nonn,base
%O 0,2
%A _Rémy Sigrist_, Apr 23 2020