A334666 For any number with binary expansion (b_1, ..., b_w), replace the i-th "1" by b_i for i = 1..A000120(n) and the j-th "0" by b_{w+1-j} for j = 1..A023416(n); the resulting binary expansion is that of a(n).

0, 1, 2, 3, 4, 6, 6, 7, 8, 12, 9, 13, 12, 14, 14, 15, 16, 24, 20, 28, 17, 25, 19, 27, 24, 28, 25, 29, 28, 30, 30, 31, 32, 48, 40, 56, 34, 50, 41, 57, 33, 49, 38, 54, 37, 53, 39, 55, 48, 56, 52, 60, 49, 57, 51, 59, 56, 60, 57, 61, 60, 62, 62, 63, 64, 96, 80

Offset: 0

Author

Rémy Sigrist, May 07 2020

Keywords

• nonn
• base

Comments

Fixed points correspond to A023758.

Examples

			For n = 41:
- the binary representation of 41 is "101001",
- the 3 1's are replaced by 1, 0, 1, respectively,
- the 3 0's are replaced by 1, 0, 0, respectively,
- hence we obtain "110001",
- and a(41) = 49.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n

Crossrefs

See A334667 for a similar sequence.

Cf. A000120, A023416, A023758.

Programs

PARI

a(n) = { my (b=binary(n), t=vector(#b), l=0, r=#b+1); for (k=1, #b, t[k] = if (b[k], b[l++], b[r--])); fromdigits(t, 2) }

Formula

A000120(a(n)) = A000120(n).

A023416(a(n)) = A023416(n).