A330081 If the binary expansion of n is (b(1), ..., b(w)), then the binary expansion of a(n) is (b(1), b(3), b(5), ..., b(6), b(4), b(2)).

0, 1, 2, 3, 4, 6, 5, 7, 8, 10, 12, 14, 9, 11, 13, 15, 16, 20, 18, 22, 24, 28, 26, 30, 17, 21, 19, 23, 25, 29, 27, 31, 32, 36, 40, 44, 34, 38, 42, 46, 48, 52, 56, 60, 50, 54, 58, 62, 33, 37, 41, 45, 35, 39, 43, 47, 49, 53, 57, 61, 51, 55, 59, 63, 64, 72, 68, 76

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers that preserves the binary length as well as the Hamming weight. See A330090 for the inverse.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

If n has w binary digits, then a^A003558(w-1)(n) = n (where a^k denotes the k-th iterate of the sequence).

Example

For n = 1234:
- the binary expansion of 1234 is "10011010010",
- odd-indexed bits are "101100",
- even-indexed bits are "01001", and in reverse order "10010",
- hence the binary expansion of a(1234) is "10110010010",
- so a(1234) = 1426.

Prog

(PARI) shuffle(v) = { my (w=vector(#v), o=0, e=#v+1); for (k=1, #v, w[if (k%2, o++, e--)]=v[k]); w }
a(n) = fromdigits(shuffle(binary(n)), 2)

Crossrefs

See A329303 for a similar sequence.

Cf. A003558, A194959, A330090 (inverse).

Sequence in context: A275119 A218252 A080541 * A072759 A361482 A257683

Adjacent sequences: A330078 A330079 A330080 * A330082 A330083 A330084

Keyword

nonn,base,easy

Author

Rémy Sigrist, Dec 01 2019

Status

approved