cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A100280 Inverse permutation to A099896.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 5, 4, 13, 12, 14, 15, 11, 10, 8, 9, 27, 26, 24, 25, 29, 28, 30, 31, 22, 23, 21, 20, 16, 17, 19, 18, 54, 55, 53, 52, 48, 49, 51, 50, 59, 58, 56, 57, 61, 60, 62, 63, 45, 44, 46, 47, 43, 42, 40, 41, 32, 33, 35, 34, 38, 39, 37, 36, 109, 108, 110, 111, 107, 106, 104
Offset: 0

Views

Author

Reinhard Zumkeller, Nov 11 2004

Keywords

Comments

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

Links

Crossrefs

Cf. A006068, A003188.

A100281 a(n) = A099896(A099896(n)).

Original entry on oeis.org

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, 84, 85, 86, 87, 81, 80, 83, 82, 94
Offset: 0

Views

Author

Reinhard Zumkeller, Nov 11 2004

Keywords

Comments

Permutation of the natural numbers with inverse A100282;
A064707(n) = a(n) for n<64.

Links

Crossrefs

Cf. A099896, A064707, A100282.

Programs

Formula

a(n) = n XOR floor(n/4) XOR floor(n/16). - Ivan Neretin, Sep 06 2017

A064707 Inverse square of permutation defined by A003188.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 13 2001

Keywords

Comments

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

Links

Crossrefs

Inverse of permutation defined by A064706. Cf. A003188.

Programs

  • MATLAB
    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

Formula

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

Extensions

More terms from David Wasserman, Aug 02 2002

A099895 XOR BINOMIAL transform of A000069 (Odious numbers).

Original entry on oeis.org

1, 3, 5, 0, 9, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129
Offset: 0

Views

Author

Paul D. Hanna, Oct 29 2004

Keywords

Comments

See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle.

Examples

			XOR difference triangle of A000069 begins:
[1],
[2,3],
[4,6,5],
[7,3,5,0],
[8,15,12,9,9],
[11,3,12,0,9,0],
[13,6,5,9,9,0,0],
[14,3,5,0,9,0,0,0],
[16,30,29,24,24,17,17,17,17],...
where A000069 is in the leftmost column,
and this sequence forms the main diagonal.

Crossrefs

Cf. A099884, A000069, A099896.

Programs

  • PARI
    {a(n)=local(B);B=0;for(i=0,n,B=bitxor(B,binomial(n,i)%2*A000069(n-i) ));B}

Formula

a(2^n) = 2^(n+1)+1 for n>0, with a(0)=1 and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A000069(n-i) and SumXOR is summation under XOR.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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