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

Offset: 0

Author

Reinhard Zumkeller, Aug 15 2010

Keywords

• nonn
• easy

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

• Index entries for sequences that are permutations of the natural numbers

Programs

R

#
maxn <- 63 # by choice
a <- 1
for(n in 1:maxn){
a[2*n  ] <- 2*a[n] + (n%%2 == 0)
a[2*n+1] <- 2*a[n] + (n%%2 != 0)}
a <- c(0, a)
# Yosu Yurramendi, May 23 2020

Formula

a(n) = A233280(A258746(n)) = A117120(A233280(n)), n > 0. - Yosu Yurramendi, Apr 10 2017 [Corrected by Yosu Yurramendi, Mar 14 2025]

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

From Alan Michael Gómez Calderón, Mar 04 2025: (Start)

a(n) = A054429(n) XOR floor(n/2) for n > 0.

a(n) = A054429(A003188(n)) for n > 0. (End)

a(n) = A154436(A054429(n)), n > 0. - Yosu Yurramendi, Mar 11 2025