Yazar "Acikel, Abdullah" seçeneğine göre listele

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    COMMON TERMS OF TRIBONACCI AND PERRIN SEQUENCES
    (Univ Miskolc Inst Math, 2022) Acikel, Abdullah; Irmak, Nurettin
    Assume that T-n is the n(th) term of Tribonacci sequence and R-m is the m(th) term of Perrin sequence. In this paper, we solve the equation T-n = R-m completely.
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    Hermite-Hadamard Type Inequalities for (?, ?; n, m)-Logarithmically and (?, ?; n, m)-Godunova-Levin-Logarithmically Convex Functions
    (Amer Inst Physics, 2016) Acikel, Abdullah; Tunc, Mevlut
    In this paper, the Authors establish some new Hermite-Hadamard type inequalities for (beta, alpha; n, m) -logarithmic and (beta, alpha; n, m)-Godunova-Levin-log-convex functions. Some special cases are also discussed.
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    Intersection of Padovan and Tribonacci sequences
    (Bulgarian Acad Science, 2023) Irmak, Nurettin; Acikel, Abdullah
    Assume that T-n is the n-th term of Tribonacci sequence and P-m is the m-th term of Padovan sequence. In this paper we solve the equation T-n = P-m completely.
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    THE k-GENERALIZED LUCAS NUMBERS CLOSE TO A POWER OF 2
    (Walter De Gruyter Gmbh, 2023) Acikel, Abdullah; Irmak, Nurettin; Szalay, Laszlo
    Let k >= 2 be a fixed integer. The k-generalized Lucas sequence {L-n((k))}(n)>=(0) starts with the positive integer initial values k, 1, 3, ..., 2(k-1)-1, and each term afterward is the sum of the k consecutive preceding elements. An integer n is said to be close to a positive integer m if n satisfies |n-m| < root m. In this paper, we combine these two concepts. We solve completely the diophantine inequality |L-n((k)) - 2(m) | < 2(m/2) in the non-negative integers k, n, and m. This problem is equivalent to the resolution of the equation L-n((k)) = 2(m) + t with the condition |t| < 2(m/2), t is an element of Z. We also discovered a new formula for L-n((k)) which was very useful in the investigation of one particular case of the problem.
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    On k-generalized Lucas sequence with its triangle
    (Tubitak Scientific & Technological Research Council Turkey, 2023) Acikel, Abdullah; Amrouche, Said; Belbachir, Hacene; Irmak, Nurettin
    In this paper, we investigate several identities of k -generalized Lucas numbers with k -generalized Fibonacci numbers. We also establish a link between generalized s -Lucas triangle and bi s nomial coefficients given by the coefficients of the development of a power of (1 + x + x2 + center dot center dot center dot + xs), with s is an element of N.
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    On perfect numbers close to Tribonacci numbers
    (Amer Inst Physics, 2018) Irmak, Nurettin; Acikel, Abdullah
    In [1], Faco and Marques gave the conditions that even perfect numbers belonging to k-generalized Fibonacci numbers. In this paper, we present alternative proof for being even perfect numbers in Tribonacci sequence. Our methods depends on p-adic order of a Tribonacci number. Moreover, we present the perfect numbers with distance 1 to Tribonacci numbers.