A334667 For any number with binary expansion (b_1, ..., b_w), replace the i-th "1" by b_{w+1-i} for i = 1..A000120(n) and the j-th "0" by b_j for j = 1..A023416(n); the resulting binary expansion is that of a(n).

0, 1, 1, 3, 2, 6, 3, 7, 4, 12, 6, 14, 3, 11, 7, 15, 8, 24, 10, 26, 9, 25, 14, 30, 6, 22, 13, 29, 7, 23, 15, 31, 16, 48, 18, 50, 17, 49, 22, 54, 18, 50, 25, 57, 21, 53, 30, 62, 12, 44, 28, 60, 14, 46, 29, 61, 7, 39, 23, 55, 15, 47, 31, 63, 32, 96, 34, 98, 33

Offset

0,4

Comments

Fixed points correspond to A000225.

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).

Example

For n = 41:
- the binary representation of 41 is "101001",
- the 3 1's are replaced by 1, 0, 0, respectively,
- the 3 0's are replaced by 1, 0, 1, respectively,
- hence we obtain "110010",
- and a(41) = 50.

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 A334666 for a similar sequence.

Cf. A000120, A000225, A023416.

Sequence in context: A144559 A155114 A038572 * A245676 A341516 A060992

Adjacent sequences: A334664 A334665 A334666 * A334668 A334669 A334670

Keyword

nonn,base

Author

Rémy Sigrist, May 08 2020

Status

approved