A233279 - OEIS

%I #38 Jun 20 2021 21:52:35

%S 0,1,2,3,4,5,7,6,8,9,11,10,15,14,12,13,16,17,19,18,23,22,20,21,31,30,

%T 28,29,24,25,27,26,32,33,35,34,39,38,36,37,47,46,44,45,40,41,43,42,63,

%U 62,60,61,56,57,59,58,48,49,51,50,55,54,52,53,64,65,67,66

%N Permutation of nonnegative integers: a(n) = A054429(A006068(n)).

%C This permutation transforms the enumeration system of positive irreducible fractions A007305/A047679 (Stern-Brocot) into the enumeration system A071766/A229742 (HCS), and the enumeration system A162909/A162910 (Bird) into A245325/A245326. - _Yosu Yurramendi_, Jun 09 2015

%H Antti Karttunen, <a href="/A233279/b233279.txt">Table of n, a(n) for n = 0..8191</a>

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

%F a(n) = A054429(A006068(n)).

%F a(n) = A006068(A063946(n)).

%F a(n) = A154435(A054429(n)).

%F a(n) = A180200(A258746(n)) = A117120(A180200(n)), n > 0. - _Yosu Yurramendi_, Apr 10 2017

%t Module[{nn = 6, s}, s = Flatten[Table[Range[2^(n + 1) - 1, 2^n, -1], {n, 0, nn}]]; Map[If[# == 0, 0, s[[#]]] &, Table[Fold[BitXor, n, Quotient[n, 2^Range[BitLength[n] - 1]]], {n, 0, 2^nn}]]] (* _Michael De Vlieger_, Apr 06 2017, after _Harvey P. Dale_ at A054429 and _Jan Mangaldan_ at A006068 *)

%o (Scheme) (define (A233279 n) (A054429 (A006068 n)))

%o (R)

%o maxrow <- 8 # by choice

%o a <- 1:3

%o for(m in 0:maxrow) for(k in 0:(2^m-1)){

%o a[2^(m+2)+            k] <- a[2^(m+1)+    k] + 2^(m+1)

%o a[2^(m+2)+        2^m+k] <- a[2^(m+1)+2^m+k] + 2^(m+1)

%o a[2^(m+2)+2^(m+1)+    k] <- a[2^(m+1)+2^m+k] + 2^(m+2)

%o a[2^(m+2)+2^(m+1)+2^m+k] <- a[2^(m+1)+   +k] + 2^(m+2)

%o }

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

%o # _Yosu Yurramendi_, Apr 05 2017

%o (R)

%o # Given n, compute a(n) by taking into account the binary representation of n

%o maxblock <- 7 # by choice

%o a <- 1

%o for(n in 2:2^maxblock){

%o   ones <- which(as.integer(intToBits(n)) == 1)

%o   nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)]

%o   anbit <- nbit

%o   for(k in 2^(0:floor(log2(length(nbit))))  )

%o     anbit <- bitwXor(anbit, c(anbit[-(1:k)], rep(0,k))) # ?bitwXor

%o   anbit[0:(length(anbit) - 1)] <- 1 - anbit[0:(length(anbit)-1)]

%o   a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))

%o }

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

%o # _Yosu Yurramendi_, May 29 2021

%o (Python)

%o from sympy import floor

%o def a006068(n):

%o     s=1

%o     while True:

%o         ns=n>>s

%o         if ns==0: break

%o         n=n^ns

%o         s<<=1

%o     return n

%o def a054429(n): return 1 if n==1 else 2*a054429(floor(n/2)) + 1 - n%2

%o def a(n): return 0 if n==0 else a054429(a006068(n)) # _Indranil Ghosh_, Jun 11 2017

%Y Inverse permutation: A233280.

%Y Cf. A006068, A054429, A063946, A154435.

%K nonn

%O 0,3

%A _Antti Karttunen_, Dec 18 2013