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

0,3

Comments

Fixed points correspond to A023758.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

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

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

Example

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.

Prog

(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) }

Crossrefs

See A334667 for a similar sequence.

Cf. A000120, A023416, A023758.

Sequence in context: A050460 A246594 A175808 * A163380 A233569 A246593

Adjacent sequences: A334663 A334664 A334665 * A334667 A334668 A334669

Keyword

nonn,base

Author

Rémy Sigrist, May 07 2020

Status

approved