A227352 Permutation of nonnegative integers: map each number by lengths of runs in its binary representation to the number in whose once left-shifted Zeckendorf representation occurs the same run lengths (in the same order) as the lengths of consecutive blocks of zeros.

0, 1, 4, 2, 7, 12, 6, 3, 11, 19, 33, 20, 10, 17, 9, 5, 18, 30, 51, 31, 54, 88, 53, 32, 16, 27, 46, 28, 15, 25, 14, 8, 29, 48, 80, 49, 83, 135, 82, 50, 87, 142, 232, 143, 86, 140, 85, 52, 26, 43, 72, 44, 75, 122, 74, 45, 24, 40, 67, 41, 23, 38, 22, 13, 47, 77

Offset

0,3

Comments

See the comments at the inverse permutation A227351 where the idea behind this mapping is explained.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A048680(A003188(n)). [The defining formula]

Moreover, this permutation effects the following correspondences:

For n>=1 A000523(n) = A102364(a(n)).

For all n, A167489(n) = A227355(a(2n+1)).

Prog

(Scheme) (define (A227352 n) (A048680 (A003188 n)))

Crossrefs

Inverse permutation: A227351. Cf. A048680, A003188.

Sequence in context: A201207 A151890 A356155 * A255140 A108167 A261690

Adjacent sequences: A227349 A227350 A227351 * A227353 A227354 A227355

Keyword

nonn,base

Author

Antti Karttunen, Jul 08 2013

Status

approved