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Square-free Lucas d -pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Czechoslovak Mathematical Journal

Let d be a fixed positive integer. A Lucas d -pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U ( P , Q ) such that the rank of N in U ( P , Q ) is exactly ( N - ε ( N ) ) / d , where ε is the signature of U ( P , Q ) . We prove here that all but a finite number of Lucas d -pseudoprimes are square free. We also prove that all but a finite number of Lucas d -pseudoprimes are Carmichael-Lucas numbers.

Squares and cubes in Sturmian sequences

Artūras Dubickas (2009)

RAIRO - Theoretical Informatics and Applications

We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.

Statistical cluster points of sequences in finite dimensional spaces

Serpil Pehlivan, A. Güncan, M. A. Mamedov (2004)

Czechoslovak Mathematical Journal

In this paper we study the set of statistical cluster points of sequences in m -dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m -dimensional spaces too. We also define a notion of Γ -statistical convergence. A sequence x is Γ -statistically convergent to a set C if C is a minimal closed set such that for every ϵ > 0 the set { k ρ ( C , x k ) ≥ ϵ } has density zero. It is shown that every statistically bounded sequence...

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