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 n-th term and the n-th missing term, and discuss a number of related sequences. (1) To whom correspondence should be addressed.

We introduce a novel fourth order linear recurrence sequence {Sn} using the two periodic binary recurrence. We call it “pellans sequence” and then we solve the system ab+ 1 = Sx, ac + 1 = Sy bc+ 1 = Sz where a < b < c are positive integers. Therefore, we extend the order of recurrence sequence for this variant diophantine equations by means of pellans sequence.

Pick any length n binary string b1b2 · · · bn and remove the first bit b1. If b2b3 · · · bn1 is a necklace then append the complement of b1 to the end of the remaining string; otherwise append b1. By repeating this process, eventually all 2 binary strings will be visited cyclically. This shift rule leads to a new de Bruijn sequence construction that can be generated in O(1)-amortized time per b...

The typical product of the star formation process is a multiple star system, most commonly a binary star. Binaries have provided the first dynamical measures of the masses of pre-main-sequence (PMS) stars. These measurements have established that T Tauri-like stars are indeed of solar mass or less, and have provided preliminary support for the mass calibrations of theoretical PMS evolutionary t...

In many communication and signal-processing systems, desired signals (sequences) are embedded in noise. Linear filters have been the primary tool for smoothing or recovering the desired signal from the degraded signal. Linear filters perform particularly well where the spectrum of the desired signal is significantly different from that of the interference. In many situations, however, the spect...

The autocorrelation function and the run structure are two basic notions for binary sequences, and they have been used as two independent criterions to characterize the randomness of binary sequences for more than 30 years. In this paper, we establish a run series expansion formula for autocorrelation function of the binary sequence and show that the autocorrelation function is in fact complete...