On Fibonacci-Like Sequences
نویسنده
چکیده
In this note, we study Fibonacci-like sequences that are defined by the recurrence Sk = a, Sk+1 = b, Sn+2 ≡ Sn+1 + Sn (mod n + 2) for all n ≥ k, where k, a, b ∈ N, 0 ≤ a < k, 0 ≤ b < k + 1, and (a, b) 6= (0, 0). We will show that the number α = 0.SkSk+1Sk+2 · · · is irrational. We also propose a conjecture on the pattern of the sequence {Sn}n≥k.
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تاریخ انتشار 2007