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

0,3

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

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

Mathematica

Array[BitXor[#, Floor[#/4]] &, 72, 0] (* Michael De Vlieger, Apr 14 2018 *)

Prog

(MATLAB) A = 1; for i = 1:7 B = A(end:-1:1); A = [A (B + length(A))]; end A(A) - 1
(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
(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
(Python)
def A064706(n): return n^ n>>2 # Chai Wah Wu, Jun 29 2022

Crossrefs

Cf. A064707 (inverse), A165211 (mod 2).

Cf. A003188, A000695, A059905, A059906.

Cf. also A054238, A163233, A302846.

Sequence in context: A101212 A232641 A258746 * A100282 A100281 A064707

Adjacent sequences: A064703 A064704 A064705 * A064707 A064708 A064709

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 13 2001

Extensions

More terms from David Wasserman, Aug 02 2002

Status

approved