

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 (n2)bit string, reversing that string, and extracting the numerical value according to Fibonacci/Zeckendorf radix.


1



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
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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 y1), (1 0 , "1 ztab y2)
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



