A331212 - OEIS

%I #41 Sep 03 2024 14:53:41

%S 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 36,15,35,21,37,24,39,88,22,41,25,42,26,43,27,44,81,28,45,29,46,77,47,

%U 78,48,79,49,80,52,83,50,82,51,89,40,92,38,90,53,84,59,85

%N 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 Rémy Sigrist, <a href="/A331212/b331212.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A331212/a331212.gp.txt">PARI program for A331212</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>

%e The first terms, alongside their base phi representation, are:

%e   n   a(n)  phi(a(n))

%e   --  ----  -------------

%e    0     0       0

%e    1     1       1

%e    2     2      10.01

%e    3     5    1000.1001

%e    4     3     100.01

%e    5     6    1010.0001

%e    6     4     101.01

%e    7     7   10000.0001

%e    8    12  100000.101001

%e    9     8   10001.0001

%e   10    13  100010.001001

%o (PARI) \\ See Links section.

%Y Cf. A109812 (binary analog), A330984.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Apr 23 2020