A371944 The binary expansion of a(n) corresponds to the ordinal transform (reduced modulo 2) of the binary expansion of n.

0, 1, 3, 2, 6, 6, 5, 5, 13, 12, 12, 13, 10, 11, 11, 10, 26, 26, 25, 25, 25, 25, 26, 26, 21, 21, 22, 22, 22, 22, 21, 21, 53, 52, 52, 53, 50, 51, 51, 50, 50, 51, 51, 50, 53, 52, 52, 53, 42, 43, 43, 42, 45, 44, 44, 45, 45, 44, 44, 45, 42, 43, 43, 42, 106, 106

Offset: 0

Author

Rémy Sigrist, Apr 13 2024

Keywords

• nonn
• base

Comments

Leading zeros are ignored.

All terms belong to A063037.

Examples

			For n = 43: the binary expansion of 43 is "101011", the corresponding ordinal transform is "1, 1, 2, 2, 3, 4", reducing modulo 2 yields "110010", the binary expansion of a(43), so a(43) = 50.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• OEIS Wiki, Ordinal transform
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A063037, A070939, A371961.

Programs

Mathematica

{0}~Join~Array[(c[0] = 1; c[1] = 1; FromDigits[Map[Mod[c[#]++, 2] &, IntegerDigits[#, 2] ], 2]) &, 120] (* Michael De Vlieger, Apr 16 2024 *)

PARI

a(n) = { my (b = binary(n), f = vector(2)); for (i = 1, #b, b[i] = f[1+b[i]]++;); fromdigits(b % 2, 2); }

Formula

A070939(a(n)) = A070939(n).

a(floor(n/2)) = floor(a(n)/2).