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A233279 Permutation of nonnegative integers: a(n) = A054429(A006068(n)). 12
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, 28, 29, 24, 25, 27, 26, 32, 33, 35, 34, 39, 38, 36, 37, 47, 46, 44, 45, 40, 41, 43, 42, 63, 62, 60, 61, 56, 57, 59, 58, 48, 49, 51, 50, 55, 54, 52, 53, 64, 65, 67, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences that are permutations of the natural numbers

FORMULA

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

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

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

a(n) = A180200(A258746(n)) = A117120(A180200(n)), n > 0. - Yosu Yurramendi, Apr 10 2017

MATHEMATICA

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 *)

PROG

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

(R)

maxrow <- 8 # by choice

a <- 1:3

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

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

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

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

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

}

(a <- c(0, a))

# Yosu Yurramendi, Apr 05 2017

(R)

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

maxblock <- 7 # by choice

a <- 1

for(n in 2:2^maxblock){

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

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

  anbit <- nbit

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

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

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

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

}

(a <- c(0, a))

# Yosu Yurramendi, May 29 2021

(Python)

from sympy import floor

def a006068(n):

    s=1

    while True:

        ns=n>>s

        if ns==0: break

        n=n^ns

        s<<=1

    return n

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

def a(n): return 0 if n==0 else a054429(a006068(n)) # Indranil Ghosh, Jun 11 2017

CROSSREFS

Inverse permutation: A233280.

Cf. A006068, A054429, A063946, A154435.

Sequence in context: A100806 A102451 A233280 * A267111 A161919 A269391

Adjacent sequences:  A233276 A233277 A233278 * A233280 A233281 A233282

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 18 2013

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)