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 1-3 of 3 results.

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

Views

Author

Reinhard Zumkeller, Nov 11 2004

Keywords

Comments

Permutation of the natural numbers with inverse A100281;
A064706(n) = a(n) for n<64.

Links

A064706 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, 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, 80, 81, 82, 83, 85, 84, 87, 86
Offset: 0

Views

Author

N. J. A. Sloane, Oct 13 2001

Keywords

Comments

Inverse of sequence A064707 considered as a permutation of the nonnegative integers.
Not the same as A100282: a(n) = A100282(n) = A100280(A100280(n)) only for n < 64. - Reinhard Zumkeller, Nov 11 2004

Links

Crossrefs

Cf. A064707 (inverse), A165211 (mod 2).
Cf. A003188, A000695, A059905, A059906.
Cf. also A054238, A163233, A302846.

Programs

  • MATLAB
    A = 1; for i = 1:7 B = A(end:-1:1); A = [A (B + length(A))]; end A(A) - 1
  • Mathematica
    Array[BitXor[#, Floor[#/4]] &, 72, 0] (* Michael De Vlieger, Apr 14 2018 *)
  • PARI
    a(n)=bitxor(n,n\4)
  • PARI
    { for (n=0, 1000, write("b064706.txt", n, " ", bitxor(n, n\4)) ) } \\ Harry J. Smith, Sep 22 2009
  • Python
    def A064706(n): return n^ n>>2 # Chai Wah Wu, Jun 29 2022
  • R
    maxn <- 63 # by choice
b <- c(1,0,0)
for(n in 4:maxn) b[n] <- b[n-1] - b[n-2] + b[n-3]
# c(1,b) is A133872
a <- 1
for(n in 1:maxn) {
a[2*n  ] <- 2*a[n] + 1 - b[n]
a[2*n+1] <- 2*a[n] +     b[n]
}
(a <- c(0,a))
# Yosu Yurramendi, Oct 25 2020

Formula

a(n) = A003188(A003188(n)).
a(n) = n XOR floor(n/4), where XOR is binary exclusive OR. - Paul D. Hanna, Oct 25 2004
a(n) = A233280(A180201(n)), n > 0. - Yosu Yurramendi, Apr 05 2017
a(n) = A000695(A003188(A059905(n))) + 2*A000695(A003188(A059906(n))). - Antti Karttunen, Apr 14 2018

Extensions

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

Views

Author

Paul D. Hanna, Nov 09 2004

Keywords

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

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.
Showing 1-3 of 3 results.

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

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