A084483 If the rightmost block of zeros in binary representation of n has an even length, then delete one 0, otherwise insert one 0 in this block.

1, 4, 3, 2, 9, 12, 7, 16, 5, 20, 19, 6, 25, 28, 15, 8, 33, 36, 11, 10, 41, 44, 39, 48, 13, 52, 51, 14, 57, 60, 31, 64, 17, 68, 67, 18, 73, 76, 23, 80, 21, 84, 83, 22, 89, 92, 79, 24, 97, 100, 27, 26, 105, 108, 103, 112, 29, 116, 115, 30, 121, 124, 63, 32, 129

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers.

Formula

a(a(n)) = n, self-inverse permutation of natural numbers.

a(n) = n iff n = 2^k - 1, k>0.

-1 <= A023416(a(n)) - A023416(n) <= 1.

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

A084484(n) = A007088(a(n)).

-1 <= A070939(a(n)) - A070939(n) <= 1.

a(2n+1) = 2a(n)+1, a(4n+2) = 8n+4, a(4n) = 2n(4-3*A035263(n)). - Ralf Stephan, Oct 09 2003

Example

n = 43 in binary 101011: insert a 0 in the rightmost block of zeros consisting of one (odd!) 0: 1010011 -> 83 = a(43).
n = 41 in binary 101001: delete a 0 from the rightmost block of zeros consisting of two (even!) 0's: 10101 -> 21 = a(41).

Mathematica

a[n_] := a[n] = If[OddQ[n], 2*a[(n - 1)/2] + 1, If[EvenQ[IntegerExponent[n, 2]], n/2, 2*n]]; Array[a, 100] (* Amiram Eldar, Jul 22 2023 *)

Crossrefs

Cf. A000120, A007088, A023416, A035263, A070939, A084484.

Sequence in context: A273991 A292828 A020703 * A266150 A276612 A058509

Adjacent sequences: A084480 A084481 A084482 * A084484 A084485 A084486

Keyword

nonn,base

Author

Reinhard Zumkeller, May 27 2003

Status

approved