A105081 a(n) = 1 + A003188(n - 1), n >= 1.

1, 2, 4, 3, 7, 8, 6, 5, 13, 14, 16, 15, 11, 12, 10, 9, 25, 26, 28, 27, 31, 32, 30, 29, 21, 22, 24, 23, 19, 20, 18, 17, 49, 50, 52, 51, 55, 56, 54, 53, 61, 62, 64, 63, 59, 60, 58, 57, 41, 42, 44, 43, 47, 48, 46, 45, 37, 38, 40, 39, 35, 36, 34, 33, 97, 98, 100, 99, 103, 104, 102

Offset: 1

Author

Philippe Deléham, Apr 28 2005

Keywords

• nonn
• easy
• look

Comments

A permutation of the natural numbers.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A066194.

Cf. A000069, A003188, A065621, A268718.

Programs

Mathematica

Nest[Join[#,Length[#]+Reverse[#]]&,{1},7] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

Python

def A105081(n): return 1+(n-1^ n-1>>1) # Chai Wah Wu, Jun 29 2022

Scheme

(define (A105081 n) (+ 1 (A003188 (- n 1)))) ;; Antti Karttunen, Feb 14 2016

Formula

a(1) = 1, a(2^k + j) = 2^k + a(2^k - j + 1) for 1 <= j <= 2^k.

A000069(a(n)) = A065621(n).

As a composition of related permutations:

a(n) = A268718(A003188(n)). - Antti Karttunen, Feb 14 2016