A373038 In the binary expansion of any nonnegative number n, say with Hamming weight w, reverse the order of the w rightmost bits.

0, 1, 2, 3, 4, 6, 5, 7, 8, 10, 9, 14, 12, 13, 11, 15, 16, 18, 17, 22, 20, 21, 19, 30, 24, 28, 26, 29, 25, 27, 23, 31, 32, 34, 33, 38, 36, 37, 35, 46, 40, 44, 42, 45, 41, 43, 39, 62, 48, 52, 50, 60, 49, 58, 54, 61, 56, 57, 53, 59, 51, 55, 47, 63, 64, 66, 65, 70

Offset

0,3

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

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

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

a(2^k - 1) = 2^k - 1 for any k >= 0.

a(2^k) = 2^k for any k >= 0.

Example

For n = 43: the binary expansion of 43 is "101011", and has Hamming weight 4, reversing the 4 rightmost bits yields "101101", so a(43) = 45.

Prog

(PARI) a(n) = { my (b = binary(n), w = hammingweight(n)); fromdigits(concat( b[1..#b-w], Vecrev(b[#b-w+1..#b])), 2); }
(Python)
def a(n): w, b = n.bit_count(), bin(n)[2:]; return int(b[:-w]+b[-w:][::-1], 2)
print([a(n) for n in range(68)]) # Michael S. Branicky, May 24 2024

Crossrefs

Cf. A000120, A059893.

Sequence in context: A361926 A332805 A332807 * A267106 A275119 A218252

Adjacent sequences: A373035 A373036 A373037 * A373039 A373040 A373041

Keyword

nonn,base,easy

Author

Rémy Sigrist, May 20 2024

Status

approved