On binary reflected Gray codes and functions

AbstractThe binary reflected Gray code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of m.This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder's result that the jth letter of the kth word of the binary reflected Gray code of length n is 2n-2n-j-1⌊2n-2n-j-1-k/2⌋mod2by replacing the binomial coefficient by k-12n-j+1+12

Mirroring and interleaving in the paperfolding sequence

Three equivalent methods of generating the paperfolding sequence are presented as well as a categorisation of runs of identical terms. We find all repeated subsequences, the largest repeated subsequences and the spacing of singles, doubles and triples throughout the sequence. The paperfolding sequence is shown to have links to the Binary Reflected Gray Code and the Stern-Brocot tree

On binary reflected Gray codes and functions

The Binary Reflected Gray Code function b is defined as follows: If m is a nonnegative integer, then b(m) is the integer obtained when initial zeros are omitted from the binary reflected Gray code of length m. This paper examines this Gray code function and its inverse and gives simple algorithms to generate both. It also simplifies Conder’s result that the jth letter of the kth word of the binary reflected Gray code of length n, is (2n − 2n−j − 1 [2n − 2n−j−1 − k/2]) mod 2, by replacing the binomial coefficient by [(k-1)/(2n-j+1)+1/2]

Locating terms in the Stern-Brocot tree

In this paper we discover an efficient method for answering two related questions involving the Stern Brocot tree: What is the jth term in the nth level of the tree? and What is the exact position of the fraction t/s in the tree? \u2

On the physical nature of halogen bonds: a QTAIM study.

International audienceIn this article, we report a detailed study on halogen bonds in complexes of CHCBr, CHCCl, CH2CHBr, FBr, FCl, and ClBr with a set of Lewis bases (NH3, OH2, SH2, OCH2, OH(-), Br(-)). To obtain insight into the physical nature of these bonds, we extensively used Bader's Quantum Theory of Atoms-in-Molecules (QTAIM). With this aim, in addition to the examination of the bond critical points properties, we apply Pendás' Interacting Quantum Atoms (IQA) scheme, which enables rigorous and physical study of each interaction at work in the formation of the halogen-bonded complexes. In particular, the influence of primary and secondary interactions on the stability of the complexes is analyzed, and the roles of electrostatics and exchange are notably discussed and compared. Finally, relationships between QTAIM descriptors and binding energies are inspected