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

Author

Reinhard Zumkeller, May 27 2003

Keywords

• nonn
• base

Examples

			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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers.

Crossrefs

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

Programs

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 *)

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