A268671 a(n) = (A268670(n)+1) / 2.

1, 2, 1, 4, 1, 2, 3, 8, 3, 2, 7, 4, 5, 6, 1, 16, 1, 6, 15, 4, 13, 14, 5, 8, 9, 10, 3, 12, 7, 2, 11, 32, 11, 2, 31, 12, 29, 30, 7, 8, 25, 26, 9, 28, 3, 10, 27, 16, 17, 18, 1, 20, 15, 6, 19, 24, 5, 14, 23, 4, 21, 22, 13, 64, 13, 22, 63, 4, 61, 62, 21, 24, 57, 58, 5, 60, 23, 14, 59, 16, 49, 50, 17, 52, 1

Offset: 1

Author

Antti Karttunen, Feb 10 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13107

Crossrefs

Cf. A001317 (positions of ones).

Cf. A268669, A268670.

Programs

Mathematica

f[n_] := Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]]; g[n_] := If[OddQ@ #, n, g[#/2]] &@ f[n]; Table[(f@ g@ n + 1)/2, {n, 85}]  (* Michael De Vlieger, Feb 12 2016, after Jan Mangaldan at A006068 *)

Scheme

(define (A268671 n) (/ (+ 1 (A268670 n)) 2))

Formula

a(n) = (A268670(n)+1) / 2.