Browsing by Author "Alkan, Altuğ"
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A computational perspective on metaFibonacci recurrence relations
Alkan, Altuğ (Piri Reis Üniversitesi, 2021)Bu doktora tezinde, bir bilgisayar cebir sistemi olan PARI/GP ile sağlanan detaylı hesaplamalı araştırmalar sayesinde metaFibonacci tekrarlama ilişkileri kavramını yeni bir yaklaşımla keşfediyoruz. İç içe geçmiş tekrarlama ... 
An exploration of solutions to two related HofstadterHuber recurrence relations
Alkan, Altuğ; Fox, Nathan; Aybar, Orhan Özgür; Akdeniz, Zehra (PergamonElsevier Science Ltd, 2020)In this study, we explore the properties of certain solutions of two HofstadterHuber recurrence relations. The first is Hofstadter's Vrecurrence, which is defined by the nested recurrence relation V(n) = V(n  V (n  1)) ... 
On a conjecture about generalized Qrecurrence
Alkan, Altuğ (Sciendo, 2018)Chaotic metaFibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of wellbehaved solutions of nested ... 
On a Generalization of Hofstadter's QSequence: A Family of Chaotic Generational Structures
Alkan, Altuğ (WileyHindawi, 2018)Hofstadter Qrecurrence is defined by the nested recurrence Q(n) = Q(n  Q(n  1)) + Q(n  Q(n  2)), and there are still many unanswered questions about certain solutions of it. In this paper, a generalization of Hofstadter's ... 
On a recursively defined sequence involving the prime counting function
Alkan, Altuğ; Booker, A.R.; Luca, F. (University of Waterloo, 2021)We prove some properties of sequence A335294 from the OnLine Encyclopedia of Integer Sequences, defined by an = ?(n)  ?(?n1 k=1ak), where ?(x) is the number of primes ? x. In particular we show that the sequence (an) ... 
On families of solutions for metafibonacci recursions related to hofstadterconway $10000 sequence
Alkan, Altuğ; Aybar, Orhan Özgür (Springer, 2020)HofstadterConway $10000 sequence is a famous metaFibonacci sequence which is defined by recurrence relation c(n) = c(c(n1)) + c(nc(n1)) with c(1)=c(2)=1. Based on its amazing fractallike structure, in this study, we ... 
On Hofstadter Heart Sequences
Alkan, Altuğ; Fox, Nathan; Aybar, Orhan Özgür (WileyHindawi, 2017)The Hofstadter Qsequence and the HofstadterConway $10000 sequence are perhaps the two best known examples of metaFibonacci sequences. In this paper, we explore an unexpected connection between them. When the Qsequence ...