1,2

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

Table of n, a(n) for n=1..65.

Index entries for sequences that are permutations of the natural numbers

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

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).

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

Sequence in context: A273991 A292828 A020703 * A266150 A276612 A058509

Adjacent sequences: A084480 A084481 A084482 * A084484 A084485 A084486

nonn

Reinhard Zumkeller, May 27 2003

approved