login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233279 Permutation of nonnegative integers: a(n) = A054429(A006068(n)). 15
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
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.
Sequence in context: A370791 A370790 A233280 * A359752 A267111 A161919
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 18 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)