A064706 - OEIS

%I #39 Jun 30 2022 08:38:15

%S 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,

%T 28,29,27,26,25,24,40,41,42,43,45,44,47,46,34,35,32,33,39,38,37,36,60,

%U 61,62,63,57,56,59,58,54,55,52,53,51,50,49,48,80,81,82,83,85,84,87,86

%N Square of permutation defined by A003188.

%C Inverse of sequence A064707 considered as a permutation of the nonnegative integers.

%C Not the same as A100282: a(n) = A100282(n) = A100280(A100280(n)) only for n < 64. - _Reinhard Zumkeller_, Nov 11 2004

%H Harry J. Smith, <a href="/A064706/b064706.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A003188(A003188(n)).

%F a(n) = n XOR floor(n/4), where XOR is binary exclusive OR. - _Paul D. Hanna_, Oct 25 2004

%F a(n) = A233280(A180201(n)), n > 0. - _Yosu Yurramendi_, Apr 05 2017

%F a(n) = A000695(A003188(A059905(n))) + 2*A000695(A003188(A059906(n))). - _Antti Karttunen_, Apr 14 2018

%t Array[BitXor[#, Floor[#/4]] &, 72, 0] (* _Michael De Vlieger_, Apr 14 2018 *)

%o (MATLAB) A = 1; for i = 1:7 B = A(end:-1:1); A = [A (B + length(A))]; end A(A) - 1

%o (PARI) a(n)=bitxor(n,n\4)

%o (PARI) { for (n=0, 1000, write("b064706.txt", n, " ", bitxor(n, n\4)) ) } \\ _Harry J. Smith_, Sep 22 2009

%o (R)

%o maxn <- 63 # by choice

%o b <- c(1,0,0)

%o for(n in 4:maxn) b[n] <- b[n-1] - b[n-2] + b[n-3]

%o # c(1,b) is A133872

%o a <- 1

%o for(n in 1:maxn) {

%o a[2*n  ] <- 2*a[n] + 1 - b[n]

%o a[2*n+1] <- 2*a[n] +     b[n]

%o }

%o (a <- c(0,a))

%o # _Yosu Yurramendi_, Oct 25 2020

%o (Python)

%o def A064706(n): return n^ n>>2 # _Chai Wah Wu_, Jun 29 2022

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

%Y Cf. A003188, A000695, A059905, A059906.

%Y Cf. also A054238, A163233, A302846.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Oct 13 2001

%E More terms from _David Wasserman_, Aug 02 2002