We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)}n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V -sequences when the product of their discriminants is a perfect square. Moreover, the inter...

A Smarandache-Fibonacci triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Clearly, it is a generalization of Fibonacci sequence and Lucas sequence. Let G be a (p, q)-graph and {S(n)|n ≥ 0} a Smarandache-Fibonacci triple. An bijection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibo...

We obtain the Binet’s formula for k-Pell-Lucas numbers and as a consequence we obtain some properties for k-Pell-Lucas numbers. Also we give the generating function for the k-Pell-Lucas sequences and another expression for the general term of the sequence, using the ordinary generating function, is provided. Mathematics Subject Classification: 11B37, 05A15, 11B83.

Let un be a nondegenerate Lucas sequence. We generalize the results of Bugeaud, Mignotte, and Siksek [6] to give a systematic approach towards the problem of determining all perfect powers in any particular Lucas sequence. We then prove a general bound on admissible prime powers in a Lucas sequence assuming the Frey-Mazur conjecture on isomorphic mod p Galois representations of elliptic curves.

The RSL continues to evolve and two faculty recruitments are in progress for molecular imaging and cognitive neuroimaging. These are major initiatives for the Department and the Lab. Molecular imaging is broadly defined as the visualization of in vivo structures that are identified on the molecular level by genetic expression or some other tagging means. The NIH has recently highlighted this fi...

A fast and simple O(logn) iteration algorithm for individual Lucas numbers is given. This is faster than using Fibonacci based methods because of the structure of Lucas numbers. Using a √ 5 conversion factor gives a faster Fibonacci algorithm because the speed up proposed in [5] also directly applies. A fast simple recursive algorithm for individual Lucas numbers is given that is O(logn).

I argue that if we are Turing machines, as the Computational Theory of Mind (CTM) holds, then we are paraconsistent, i.e. we do not implement classical logic as canonical versions of the CTM generally hold (or assume). I then show that this claim presents a serious challenge to the Lucas-Penrose argument (Lucas 1961, Penrose 1989, 94), as it collapses Lucas-Penrose into a disjunction (in a mann...

The objective of this study was to evaluate and compare the complications of cardiopulmonary resuscitation after manual or mechanical chest compressions in a swine model of ventricular fibrillation. In this retrospective study, 106 swine were treated with either manual (n=53) or mechanical chest compressions with the LUCAS device (n=53). All swine cadavers underwent necropsy. The animals with n...