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

Author

Antti Karttunen, Jul 08 2013

Keywords

• nonn
• base

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

Crossrefs

Inverse permutation: A227351. Cf. A048680, A003188.

Programs

Scheme

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

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)).