A257962 - OEIS

%I #12 Jun 16 2015 13:32:08

%S 0,0,1,0,2,1,0,3,2,1,4,0,5,3,2,7,1,6,4,0,8,5,3,11,2,10,7,1,9,6,4,12,0,

%T 13,8,5,18,3,16,11,2,15,10,7,20,1,14,9,6,19,4,17,12,0,21,13,8,29,5,26,

%U 18,3,24,16,11,32,2,23,15,10,31,7,28,20,1,22,14

%N List of successive permutations of the numbers [0,F(n)) achieved by writing the numbers in the Fibonacci/Zeckendorf radix in the form of an (n-2)-bit string, reversing that string, and extracting the numerical value according to Fibonacci/Zeckendorf radix.

%C This sequence divides into blocks of length F(n), n = 1, 2, 3, 4, 5, ... (so F(n) = 1, 2, 3, 5, 8, ...)

%H Peter G. Anderson, <a href="/A257962/b257962.txt">Table of n, a(n) for n = 0..317808</a>

%e This is an irregular array, the first few rows of which are:

%e 0;

%e 0, 1;

%e 0, 2, 1;

%e 0, 3, 2, 1, 4;

%e 0, 5, 3, 2, 7, 1, 6, 4;

%e 0, 8, 5, 3, 11, 2, 10, 7, 1, 9, 6, 4, 12;

%e 0, 13, 8, 5, 18, 3, 16, 11, 2, 15, 10, 7, 20, 1, 14, 9, 6, 19, 4, 17, 12;

%o (J)

%o The function ztab in the j language computes a table of Zeckendorf representations for the integers [0,F(n+2))

%o ztab =: 3 : 0

%o         if. y = 1 do. 2 1 $ 0 1

%o         elseif. y = 2 do. 3 2 $ 0 0 0 1 1 0

%o         elseif. do. (0  ,"1 ztab y-1), (1 0 ,"1 ztab y-2)

%o         end.

%o )

%o    ztab 5

%o 0 0 0 0 0

%o 0 0 0 0 1

%o 0 0 0 1 0

%o 0 0 1 0 0

%o 0 0 1 0 1

%o 0 1 0 0 0

%o 0 1 0 0 1

%o 0 1 0 1 0

%o 1 0 0 0 0

%o 1 0 0 0 1

%o 1 0 0 1 0

%o 1 0 1 0 0

%o 1 0 1 0 1

%o Then forming the inner product with the Fibonacci numbers reversed (i.e., evaluating in the Fibonacci radix backwards) give the permutation:

%o    1 2 3 5 8 +/ . * "1 ztab 5

%o 0 8 5 3 11 2 10 7 1 9 6 4 12

%Y Cf. A014417, A257691.

%K nonn,tabf,base

%O 0,5

%A _Peter G. Anderson_, May 14 2015