bibkey: stephan2003a059894
authors: Marc LeBrun; Ralf Stephan
year: 2003
title: "OEIS A059894, complement and reverse all but the most significant bit"
doi: null
url: https://oeis.org/A059894
claim: "A059894 %N: Complement and reverse the order of all but the most significant bit in binary expansion of n. n = 1ab..yz -> 1ZY..BA = a(n), where A = 1-a, B = 1-b, ... . A059894 %F: a(1) = 1, a(2n) = a(n) + 2^(floor(log_2(n))+1), a(2n+1) = a(n) + 2^floor(log_2(n)) (conjectured). - _Ralf Stephan_, Aug 21 2003 A059894 %F: A000120(a(n)) = A000120(A054429(n)) = A023416(n) + 1 (conjectured). - _Ralf Stephan_, Oct 05 2003"
strata_touched:
  - D5/S1/Digit/StephanComplementReverseRecurrence
license: citation-only
triage: anchor

OEIS A059894

Marc LeBrun’s sequence complements and reverses the lower binary bits while retaining the leading one. Ralf Stephan’s two 2003 formula lines conjecture recurrences and equalities between binary digit counts.

Verified locator

URL: https://oeis.org/A059894

NAME (%N, verbatim):

Complement and reverse the order of all but the most significant bit in binary expansion of n. n = 1ab..yz -> 1ZY..BA = a(n), where A = 1-a, B = 1-b, … .

FORMULA (%F, verbatim):

a(1) = 1, a(2n) = a(n) + 2^(floor(log_2(n))+1), a(2n+1) = a(n) + 2^floor(log_2(n)) (conjectured). - Ralf Stephan, Aug 21 2003

FORMULA (%F, verbatim):

A000120(a(n)) = A000120(A054429(n)) = A023416(n) + 1 (conjectured). - Ralf Stephan, Oct 05 2003

AUTHOR (%A, verbatim):

Marc LeBrun, Feb 06 2001

The locator text is supplied by the orchestrator’s 2026-09-15 source reading. It is ASSUMED-UNVERIFIED in the offline implementation seat. This note quotes only the definition, two conjectures, and attribution; it redistributes no sequence data.