A generalization of the well-known Fibonacci sequence is k?Fibonacci whose first k terms are 0,…,0,1 and each term afterwards sum preceding terms. In this paper, we find all k-Fibonacci numbers that curious (i.e., base ten representation have form a?ab?ba?a). This work continues extends prior result Trojovský, who found with a prescribed block digits, Alahmadi et al., searched for numbers, whic...

Among numerical sequences, the Fibonacci numbers Fn have achieved a kind of celebrity status. Indeed, Koshy gushingly refers to them as one of the “two shining stars in the vast array of integer sequences” [16, p. xi]. The second of Koshy’s “shining stars” is the Lucas numbers, a close relative of the Fibonacci numbers, about which we will say more below. The Fibonacci numbers are famous for po...

Here, we investigate the Fibonacci numbers whose sum of aliquot divisors is also a Fibonacci number (the prime Fibonacci numbers have this property).

In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized Fibonacci numbers.