A180201 - OEIS

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A180201

Inverse permutation to A180200.

0, 1, 2, 3, 5, 4, 6, 7, 11, 10, 8, 9, 13, 12, 14, 15, 23, 22, 20, 21, 17, 16, 18, 19, 27, 26, 24, 25, 29, 28, 30, 31, 47, 46, 44, 45, 41, 40, 42, 43, 35, 34, 32, 33, 37, 36, 38, 39, 55, 54, 52, 53, 49, 48, 50, 51, 59, 58, 56, 57, 61, 60, 62, 63, 95, 94, 92, 93, 89, 88, 90, 91, 83

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

A180199(n) = a(a(n));

a(A180198(n)) = A180198(a(n)) = A180200(n);

a(A075427(n)) = A075427(n).

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

LINKS

Table of n, a(n) for n=0..72.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A258746(A233280(n)) = A233280(A117120(n)), n > 0. - Yosu Yurramendi, Apr 10 2017

a(0) = 0, a(1) = 1, for n > 0 a(2*n) = 2*a(n) + [n even], a(2*n + 1) = 2*a(n) + [n odd]. - Yosu Yurramendi, May 23 2020

PROG

(R)

maxn <- 63 # by choice

a <- 1

for(n in 1:maxn){

a[2*n ] <- 2*a[n] + (n%%2 == 0)