The random Fibonacci sequence is defined by t1 = t2 = 1 and tn = ±tn−1 + tn−2, for n > 3, where each ± sign is chosen at random with probability P (+) = P (−) = 12 . Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate 1.13198824 . . . . We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choos...

Abstract— Identification whether a certain number belongs to either Fibonacci or Lucas sequence is computationally intense task in the sense that the sequence itself need to be written from the beginning until the requested number. In this paper we present a method of detecting whether a certain number is of Lucas or Fibonacci sequence as well as introduce relationships between such sequences. ...

Abstract—Study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling vague and incomplete data. A variety of forecasting models have devoted to improve forecasting accuracy. Recently, Fuzzy time-series based on Fibonacci sequence has been proposed as a new fuzzy time series model which incorporates the concept of the Fibonacci sequence, the f...