A257962 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.

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

Offset: 0

Author

Peter G. Anderson, May 14 2015

Keywords

• nonn
• tabf
• base

Comments

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

Examples

			This is an irregular array, the first few rows of which are:
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, 13, 8, 5, 18, 3, 16, 11, 2, 15, 10, 7, 20, 1, 14, 9, 6, 19, 4, 17, 12;
		

Links

• Peter G. Anderson, Table of n, a(n) for n = 0..317808

Crossrefs

Cf. A014417, A257691.

Programs

J

The function ztab in the j language computes a table of Zeckendorf representations for the integers [0,F(n+2))
ztab =: 3 : 0
        if. y = 1 do. 2 1 $ 0 1
        elseif. y = 2 do. 3 2 $ 0 0 0 1 1 0
        elseif. do. (0  ,"1 ztab y-1), (1 0 ,"1 ztab y-2)
        end.
)
   ztab 5
0 0 0 0 0
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 0 1
0 1 0 0 0
0 1 0 0 1
0 1 0 1 0
1 0 0 0 0
1 0 0 0 1
1 0 0 1 0
1 0 1 0 0
1 0 1 0 1
Then forming the inner product with the Fibonacci numbers reversed (i.e., evaluating in the Fibonacci radix backwards) give the permutation:
   1 2 3 5 8 +/ . * "1 ztab 5
0 8 5 3 11 2 10 7 1 9 6 4 12