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    On perfect numbers close to Tribonacci numbers
    (American Institute of Physics Inc., 2018) Irmak N.; Açikel A.
    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. © 2018 Author(s).
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    The rank of apparition of powers of Lucas sequence
    (TUBITAK, 2018) Ray P.K.; Irmak N.; Patel B.K.
    This note is devoted to studying the divisibility relation uk+1 n |um for a least positive integer m, where (Un)n?0 is a nondegenerate Lucas sequence with characteristic polynomial x2 - ax - b, for some relatively prime integers a and b. ©TÜBITAK.
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    Tribonacci numbers close to the sum 2a + 3b + 5C
    (Mathematica Scandinavica, 2016) Irmak N.; Szalay L.
    We show that there are exactly 22 solutions to the inequalities 0 ? Tn - 2a - 3b - 5C ? 10. where Tn denotes thenth term (n ? 0) of the Tribonacci sequence, andO ? a,b ? c are integers. All the solutions are explicitly determined.
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    Two-periodic ternary recurrences and their Binet-formula
    (2012) Alp M.; Irmak N.; Szalay L.
    The properties of k-periodic binary recurrences have been discussed by several authors. In this paper, we define the notion of the two-periodic ternary linear recurrence. First we follow Cooper's approach to obtain the corresponding recurrence relation of order six. Then we provide explicit formulae linked to the three possible cases.