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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.
4
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
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, May 27 2003
STATUS
approved