A100281 -id:A100281 - cp's OEIS frontend

A064707 Inverse square of permutation defined by A003188.

0, 1, 2, 3, 5, 4, 7, 6, 10, 11, 8, 9, 15, 14, 13, 12, 21, 20, 23, 22, 16, 17, 18, 19, 31, 30, 29, 28, 26, 27, 24, 25, 42, 43, 40, 41, 47, 46, 45, 44, 32, 33, 34, 35, 37, 36, 39, 38, 63, 62, 61, 60, 58, 59, 56, 57, 53, 52, 55, 54, 48, 49, 50, 51, 85, 84, 87, 86, 80, 81, 82, 83

Offset: 0

N. J. A. Sloane, Oct 13 2001

Not the same as A100281: a(n)=A100281(n)=A099896(A099896(n)) only for n<64. - Reinhard Zumkeller, Nov 11 2004

Inverse of permutation defined by A064706. Cf. A003188.

A = 1; for i = 1:7 B = A(end:-1:1); A = [A (B + length(A))]; end C = A(A); for i = 1:128 A(C(i)) = i - 1; end A

a(n) = A180200(A233279(n)), n > 0. - Yosu Yurramendi, Apr 05 2017

More terms from David Wasserman, Aug 02 2002

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

Original entry on oeis.org

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

Paul D. Hanna, Nov 09 2004

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

Cf. A003188, A099884.

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

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

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.

A100282 a(n) = A100280(A100280(n)).

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 7, 6, 10, 11, 8, 9, 15, 14, 13, 12, 20, 21, 22, 23, 17, 16, 19, 18, 30, 31, 28, 29, 27, 26, 25, 24, 40, 41, 42, 43, 45, 44, 47, 46, 34, 35, 32, 33, 39, 38, 37, 36, 60, 61, 62, 63, 57, 56, 59, 58, 54, 55, 52, 53, 51, 50, 49, 48, 81, 80, 83, 82, 84, 85, 86, 87, 91

Offset: 0

Reinhard Zumkeller, Nov 11 2004

Permutation of the natural numbers with inverse A100281;

A064706(n) = a(n) for n<64.

cp's OEIS Frontend

A064707 Inverse square of permutation defined by A003188.

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

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Mathematica

PARI

Formula

A100282 a(n) = A100280(A100280(n)).

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