# Linked Questions

16 questions linked to/from Fibonacci Sequence Generator
2answers
193 views

### How to define nested recursive sequence? [duplicate]

I have Conway's Challenge sequence at hand i.e. $a_n=a_{a_{n-1}}+a_{n-a_{n-1}}$ for $\ n \geq 3$ and $a_1=a_2=1$. I have basically no idea how to define this in Mathematica.
0answers
106 views

### Optimization of recursive functions by using the //. operator [duplicate]

In some cases, recursion in Mathematica (without storing values) is not very efficient. For example, the recursive implementation of Fibonacci numbers (version which doesn't store the values) : <...
0answers
51 views

### Fibonacci series up to 300 terms [duplicate]

I tried to generate a list of Fibonacci numbers up to 300 terms and gets a runtime error. f[0]=0; f[1]=1; f[x_]:=f[x-1]+f[x-2]; Table[f[x],{x,1,300}] Is there ...
8answers
8k views

### Can one identify the design patterns of Mathematica?

... or are they unnecessary in such a high-level language? I've been thinking about programming style, coding standards and the like quite a bit lately, the result of my current work on a mixed .Net/...
9answers
4k views

### How can I make a Tribonacci sequence in the form of a list?

How can I make a Tribonacci sequence that is in listing form? it suppose to look like the Fibonacci sequence but I couldn't get ...
6answers
5k views

### Recursively appending elements to a list

In wanting to demonstrate the power of Mathematica, I wanted to show my 11-year-old son how we could validate that his sequences homework was correct. We could generate the next value in sequence in a ...
5answers
5k views

In engineering problems, I am always seeing many recursion formula. For instance, In the book "The NURBS book", I discovered many recursion formula Fibonacci $$f(... 3answers 1k views ### How can I program the last digits of Fibonacci numbers? Is there a way to compute the last digits of an arbitrarily large Fibonacci number? For the 10^nth Fibonacci number, we can just find the 2^n-th Fibonacci number (if that isn't too large) \bmod n... 4answers 4k views ### High Fibonacci numbers [duplicate] When I investigate Fibonacci's series fib[n_] := fib[n] = fib[n - 1] + fib[n - 2] fib[0] = fib[1] = 1; Block[{RecursionLimit = 10^4}, fib[10^3]] I can evaluate ... 1answer 2k views ### Relative performance of the Julia language I was just reviewing the Mathematica benchmark code linked from the Julia language home page http://julialang.org/. The stated goal of the benchmarks is to test the performance of specific algorithms, ... 5answers 362 views ### Calculating N-th step of recurrent sequence I am figuring out how to calculate the n-th step of a square root approximation sequence:$$x_{n+1} = \frac12\left(x_{n} + \frac{a}{x_n}\right),$$where a is a number the root of which is to be ... 2answers 232 views ### Unset while running recursion I am trying to run a recursive definition while at the same time clearing previously found values, so my memory is not completely consumed. I found this: How to clear parts of a memoized function? ... 2answers 266 views ### ReplaceRepeated as a Looping construct? There are a lot of discussions about looping constructs (notable example here). Wolfram language guides, as usually, contain most relevant links. Looping constructs guide has the following part on the ... 3answers 144 views ### How can I make custom accumulated sequences like the following? First of all, I don't really know how to formulate the question, so if you understand my question and know a better way to phrase it, please revise. I have the following Matrixes: ... 2answers 120 views ### Solving an inequality involving the Fibonacci function How can I solve an inequality that involves the Fibonacci function? For instance, say I want to determine for which values of n we get that$$F_n\leqslant 1000. I tried to use ...

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