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A331212 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common 1 in their base phi representations.

%I A331212 #41 Sep 03 2024 14:53:41
%S A331212 0,1,2,5,3,6,4,7,12,8,13,10,16,9,14,34,11,17,30,18,31,19,32,20,33,23,
%T A331212 36,15,35,21,37,24,39,88,22,41,25,42,26,43,27,44,81,28,45,29,46,77,47,
%U A331212 78,48,79,49,80,52,83,50,82,51,89,40,92,38,90,53,84,59,85
%N A331212 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) and a(n+1) have no common 1 in their base phi representations.
%H A331212 Rémy Sigrist, <a href="/A331212/b331212.txt">Table of n, a(n) for n = 0..10000</a>
%H A331212 Rémy Sigrist, <a href="/A331212/a331212.gp.txt">PARI program for A331212</a>
%H A331212 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>
%e A331212 The first terms, alongside their base phi representation, are:
%e A331212   n   a(n)  phi(a(n))
%e A331212   --  ----  -------------
%e A331212    0     0       0
%e A331212    1     1       1
%e A331212    2     2      10.01
%e A331212    3     5    1000.1001
%e A331212    4     3     100.01
%e A331212    5     6    1010.0001
%e A331212    6     4     101.01
%e A331212    7     7   10000.0001
%e A331212    8    12  100000.101001
%e A331212    9     8   10001.0001
%e A331212   10    13  100010.001001
%o A331212 (PARI) \\ See Links section.
%Y A331212 Cf. A109812 (binary analog), A330984.
%K A331212 nonn,base
%O A331212 0,3
%A A331212 _Rémy Sigrist_, Apr 23 2020