Yazar "Alkan, Altuğ" için listeleme
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A computational perspective on meta-Fibonacci recurrence relations
Alkan, Altuğ (Piri Reis Üniversitesi, 2021)Bu doktora tezinde, bir bilgisayar cebir sistemi olan PARI/GP ile sağlanan detaylı hesaplamalı araştırmalar sayesinde meta-Fibonacci tekrarlama ilişkileri kavramını yeni bir yaklaşımla keşfediyoruz. İç içe geçmiş tekrarlama ... -
An exploration of solutions to two related Hofstadter-Huber recurrence relations
Alkan, Altuğ; Fox, Nathan; Aybar, Orhan Özgür; Akdeniz, Zehra (Pergamon-Elsevier Science Ltd, 2020)In this study, we explore the properties of certain solutions of two Hofstadter-Huber recurrence relations. The first is Hofstadter's V-recurrence, which is defined by the nested recurrence relation V(n) = V(n - V (n - 1)) ... -
On a conjecture about generalized Q-recurrence
Alkan, Altuğ (Sciendo, 2018)Chaotic meta-Fibonacci sequences which are generated by intriguing examples of nonlinear recurrences still keep their mystery although substantial progress has been made in terms of well-behaved solutions of nested ... -
On a Generalization of Hofstadter's Q-Sequence: A Family of Chaotic Generational Structures
Alkan, Altuğ (Wiley-Hindawi, 2018)Hofstadter Q-recurrence 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 On-Line Encyclopedia of Integer Sequences, defined by an = ?(n) - ?(?n-1 k=1ak), where ?(x) is the number of primes ? x. In particular we show that the sequence (an) ... -
On families of solutions for meta-fibonacci recursions related to hofstadter-conway $10000 sequence
Alkan, Altuğ; Aybar, Orhan Özgür (Springer, 2020)Hofstadter-Conway $10000 sequence is a famous meta-Fibonacci sequence which is defined by recurrence relation c(n) = c(c(n-1)) + c(n-c(n-1)) with c(1)=c(2)=1. Based on its amazing fractal-like structure, in this study, we ... -
On Hofstadter Heart Sequences
Alkan, Altuğ; Fox, Nathan; Aybar, Orhan Özgür (Wiley-Hindawi, 2017)The Hofstadter Q-sequence and the Hofstadter-Conway $10000 sequence are perhaps the two best known examples of meta-Fibonacci sequences. In this paper, we explore an unexpected connection between them. When the Q-sequence ...
