A382113 Gray code transformation of the Zeckendorf representation of n.

0, 1, 3, 6, 5, 11, 10, 8, 19, 18, 16, 13, 14, 32, 31, 29, 26, 27, 21, 22, 24, 53, 52, 50, 47, 48, 42, 43, 45, 34, 35, 37, 40, 39, 87, 86, 84, 81, 82, 76, 77, 79, 68, 69, 71, 74, 73, 55, 56, 58, 61, 60, 66, 65, 63, 142, 141, 139, 136, 137, 131, 132, 134, 123, 124

Offset

0,3

Links

Table of n, a(n) for n=0..64.

Formula

a(n) = A022290(A006068(A003714(n))). In other words, take n, calculate its Zeckendorf representation, find the Gray code equivalent of that binary string; then regard it as the Zeckendorf representation of a number (even though it might have two consecutive 1's).

Example

For n = 5: its Zeckendorf representation is 1000; the Gray code equivalent is 1111, which evaluates to 1+2+3+5=11. So a(5) = 11.

Crossrefs

Cf. A003714, A006068, A022290, A382112.

Cf. A382116 (terms sorted).

Sequence in context: A093419 A160049 A096620 * A331124 A299209 A007479

Adjacent sequences: A382110 A382111 A382112 * A382114 A382115 A382116

Keyword

nonn,easy

Author

Jeffrey Shallit, Mar 16 2025

Status

approved