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

0,5

Comments

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

Links

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

Example

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;

Prog

(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

Crossrefs

Cf. A014417, A257691.

Sequence in context: A025655 A022336 A019586 * A176095 A295508 A260672

Adjacent sequences: A257959 A257960 A257961 * A257963 A257964 A257965

Keyword

nonn,tabf,base

Author

Peter G. Anderson, May 14 2015

Status

approved