Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.6

Sloping Binary Numbers: A New Sequence Related to the Binary Numbers

David Applegate
Internet and Network Systems Research Center
AT&T Shannon Labs
180 Park Avenue
Florham Park, NJ 07932-0971
USA

Benoit Cloitre
13 rue Pinaigrier
Tours 3700
FRANCE

Philippe Deléham
Lycée Polyvalent des Iles
BP 887
98820 Wé Lifou
NEW CALEDONIA

N. J. A. Sloane
Internet and Network Systems Research Center
AT&T Shannon Labs
180 Park Avenue
Florham Park, NJ 07932-0971
USA

Abstract: If the list of binary numbers is read by upward-sloping diagonals, the resulting "sloping binary numbers" 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) have some surprising properties. We give formulae for the nth term and the nth missing term, and discuss a number of related sequences.

(Concerned with sequences A034797 A102370 A102371 A103122 A103127 A103185 A103192 A103202 A103205 A103318 A103528 A103529 A103530 A103542 A103543 A103581 A103582 A103583 A103584 A103585 A103586 A103587 A103588 A103589 A103615 A103621 A103745 A103747 A103813 A103842 A103863 A104234 A104235 A104378 A104401 A104403 A104489 A104490 A104853 A104893 A105023 A105024 A105025 A105026 A105027 A105028 A105029 A105030 A105031 A105032 A105033 A105034 A105035 A105085 A105104 A105108 A105109 A105153 A105154 A105158 A105159 A105228 A105229 A105271 and A106623 .)

Received May 14 2005; revised version received August 2 2005. Published in Journal of Integer Sequences August 3 2005.