A099896 A permutation of the natural numbers where a(n) = n XOR [n/2] XOR [n/4].

1, 3, 2, 7, 6, 4, 5, 14, 15, 13, 12, 9, 8, 10, 11, 28, 29, 31, 30, 27, 26, 24, 25, 18, 19, 17, 16, 21, 20, 22, 23, 56, 57, 59, 58, 63, 62, 60, 61, 54, 55, 53, 52, 49, 48, 50, 51, 36, 37, 39, 38, 35, 34, 32, 33, 42, 43, 41, 40, 45, 44, 46, 47, 112, 113, 115, 114, 119, 118, 116

Offset: 1

Author

Paul D. Hanna, Nov 09 2004

Keywords

• nonn
• look

Comments

Related to Gray code numbers (A003188) since A003188(n) = n XOR [n/2].

Inverse: A100280; A100281(n) = a(a(n)). - Reinhard Zumkeller, Nov 11 2004

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003188, A099884.

Programs

Mathematica

Array[BitXor[BitXor[#,Floor[#/2]],Floor[#/4]]&,70] (* Harvey P. Dale, Aug 10 2012 *)

PARI

a(n)=bitxor(bitxor(n,n\2),n\4)

Formula

XOR BINOMIAL transform begins: B={1, 2, 3, 7, 7, 0, 0, 14, 14, 0, 0, ...} and continues with B(2^k)=B(2^k+1)=7*2^(k-2) (for k>=2) and zeros elsewhere.