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A334374 Lexicographically earliest sequence of nonnegative integers such that for any distinct i and j, a(i) = a(j) implies that the Zeckendorf representations of i and of j have no common term.

%I A334374 #9 Apr 27 2020 23:58:59
%S A334374 0,0,0,0,1,0,2,1,0,3,2,4,5,0,4,3,2,6,5,7,8,0,8,4,3,9,6,10,11,1,12,7,
%T A334374 13,14,0,11,5,7,15,3,13,9,6,16,10,8,17,1,18,12,19,20,14,21,22,0,19,6,
%U A334374 10,22,4,23,15,9,24,18,11,25,13,26,16,27,28,17,29
%N A334374 Lexicographically earliest sequence of nonnegative integers such that for any distinct i and j, a(i) = a(j) implies that the Zeckendorf representations of i and of j have no common term.
%C A334374 This sequence is a variant of A279125.
%H A334374 Rémy Sigrist, <a href="/A334374/b334374.txt">Table of n, a(n) for n = 0..10000</a>
%H A334374 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeckendorf&#39;s_theorem">Zeckendorf's theorem</a>
%H A334374 Rémy Sigrist, <a href="/A334374/a334374.gp.txt">PARI program for A334374</a>
%F A334374 a(n) = 0 iff n is a Fibonacci number (A000045).
%e A334374 The first terms, alongside their Zeckendorf representation in binary, are:
%e A334374   n   a(n)  bin(A003714(a(n)))
%e A334374   --  ----  ------------------
%e A334374    0     0                   0
%e A334374    1     0                   1
%e A334374    2     0                  10
%e A334374    3     0                 100
%e A334374    4     1                 101
%e A334374    5     0                1000
%e A334374    6     2                1001
%e A334374    7     1                1010
%e A334374    8     0               10000
%e A334374    9     3               10001
%e A334374   10     2               10010
%e A334374   11     4               10100
%e A334374   12     5               10101
%e A334374   13     0              100000
%o A334374 (PARI) See Links section.
%Y A334374 Cf. A000045, A279125.
%K A334374 nonn
%O A334374 0,7
%A A334374 _Rémy Sigrist_, Apr 25 2020