Generalized Lucas Numbers Which are Concatenations of Two Repdigits
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DOI: 10.1007/s00025-021-01456-9
Abstract: A generalization of the well–known Lucas sequence is the k–Lucas sequence with some fixed integer $$k\ge 2$$ . The first k terms of this sequence are $$0,\ldots ,0,2,1$$ , and each term afterwards is the… read more here.
Keywords: generalized lucas; concatenations two; lucas numbers; two repdigits ... See more keywords
Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials
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DOI: 10.1080/00927872.2019.1576186
Abstract: Abstract In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the… read more here.
Keywords: lucas polynomials; polynomials relationships; relationships fibonacci; generalized lucas ... See more keywords
Pythagorean triples containing generalized Lucas numbers
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DOI: 10.3906/mat-1702-102
Abstract: Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper,… read more here.
Keywords: triples containing; pythagorean triples; generalized lucas; lucas numbers ... See more keywords
Repdigits as sums of two generalized Lucas numbers
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DOI: 10.3906/mat-2011-59
Abstract: A generalization of the well–known Lucas sequence is the k -Lucas sequence with some fixed integer k ≥ 2 . The first k terms of this sequence are 0, . . . , 0, 2,… read more here.
Keywords: generalized lucas; sums two; lucas; repdigits sums ... See more keywords