A332565 - OEIS

%I #34 Apr 27 2020 08:16:26

%S 0,1,2,3,5,4,7,8,6,10,13,9,15,11,14,21,12,18,22,16,23,17,26,34,19,24,

%T 20,25,36,27,37,28,35,29,38,31,39,30,41,32,40,55,33,47,56,42,57,43,58,

%U 44,59,49,60,45,61,50,62,46,68,89,48,63,51,65,52,64,54,66

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

%C This sequence is a permutation of the natural numbers.

%H Rémy Sigrist, <a href="/A332565/b332565.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A332565/a332565.gp.txt">PARI program for A332565</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A003714(a(n)) AND A003714(a(n+1)) = 0 for any n >= 0 (where AND denotes the bitwise AND operator).

%e The first terms, alongside their Zeckendorf representation in binary, are:

%e   n   a(n)  bin(A003714(a(n)))

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

%e    0     0                   0

%e    1     1                   1

%e    2     2                  10

%e    3     3                 100

%e    4     5                1000

%e    5     4                 101

%e    6     7                1010

%e    7     8               10000

%e    8     6                1001

%e    9    10               10010

%e   10    13              100000

%o (PARI) See Links section.

%Y Cf. A003714, A109812 (binary analog), A332022.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Apr 23 2020