A064706 Square of permutation defined by A003188.

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

Author

N. J. A. Sloane, Oct 13 2001

Keywords

• nonn
• easy

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

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for sequences that are permutations of the natural numbers

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