A371944 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

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

OFFSET

0,3

COMMENTS

Leading zeros are ignored.

All terms belong to A063037.

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

FORMULA

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

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A063037, A070939, A371961.

Sequence in context: A104633 A102022 A064684 * A098071 A347741 A347742

Adjacent sequences: A371941 A371942 A371943 * A371945 A371946 A371947

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Apr 13 2024

STATUS

approved