A233280 Permutation of nonnegative integers: a(n) = A003188(A054429(n)).

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 11, 10, 14, 15, 13, 12, 16, 17, 19, 18, 22, 23, 21, 20, 28, 29, 31, 30, 26, 27, 25, 24, 32, 33, 35, 34, 38, 39, 37, 36, 44, 45, 47, 46, 42, 43, 41, 40, 56, 57, 59, 58, 62, 63, 61, 60, 52, 53, 55, 54, 50, 51, 49, 48, 64, 65, 67, 66

Offset: 0

Author

Antti Karttunen, Dec 18 2013

Keywords

• nonn

Comments

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

Crossrefs

Inverse permutation: A233279.

Cf. A000069, A001969, A003188, A054429, A063946, A154436.

Similarly constructed permutation pairs: A003188/A006068, A135141/A227413, A232751/A232752, A233275/A233276, A233277/A233278, A193231 (self-inverse).

Programs

Python

from sympy import floor
def a003188(n): return n^(n>>1)
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 a003188(a054429(n)) # Indranil Ghosh, Jun 11 2017

R

maxrow <- 8 # by choice
a <- 1
for(m in 0:maxrow) for(k in 0:(2^m-1)){
a[2^(m+1)+    k] <- a[2^m+      k] + 2^m
a[2^(m+1)+2^m+k] <- a[2^(m+1)-1-k] + 2^(m+1)
}
a
# Yosu Yurramendi, Apr 05 2017

Scheme

(define (A233280 n) (A003188 (A054429 n)))
;; Alternative version, based on entangling even & odd numbers with odious and evil numbers:
(definec (A233280 n) (cond ((< n 2) n) ((even? n) (A000069 (+ 1 (A233280 (/ n 2))))) (else (A001969 (+ 1 (A233280 (/ (- n 1) 2)))))))

Formula

a(n) = A003188(A054429(n)).

a(n) = A063946(A003188(n)).

a(n) = A054429(A154436(n)).

a(0)=0, a(1)=1, and otherwise, a(2n) = A000069(1+a(n)), a(2n+1) = A001969(1+a(n)). [A recurrence based on entangling even & odd numbers with odious and evil numbers]

a(n) = A258746(A180201(n)) = A180201(A117120(n)), n > 0. - Yosu Yurramendi, Apr 10 2017