h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

4181

I bet most Americans think the "Fibonacci Series" is an Italian baseball trophy...

6765



It's amazing how easy it is to work American insults into threads

B

10946

Joins in

17711

Is anyone still working these out in their heads?

B

28657

I think

46,368

and I used a calculator - mental arithmetic is way beyond Monday morning brain activity for me

75,025

This could become a useful reference in future. If you ever get asked "what's the 25th number in the Fibonacci series?", you'll know exactly where to find it

B

121,393

I only did that so I could ask a Fibonacci related question:

I understood that the series only had to begin with two seeds? do they have to be 0 and 1? Could it be 6 and 7? or 5 and 34?

In which case there is no 25th number unless you specify what the seeds are.

I'm confused now.

196,418

I was expecting this thread to get dumped to the bottom of Ask Hootoo.

Liam.

317,811

It's amazing what'll keep going if we're provoked.

My understanding of the Fibonacci sequence is that it specifically grows out of a field of nulls, needing only the smallest seed (ie. 1). Obviously, it'd work with 6 & 7, or whatever, but it wouldn't be a Fibonacci series, just a bunch of numbers you're adding together.

B

Ah, Liam, I was starting to wonder where you had got to after kicking this off ...

I think that the Fibonacci sequence is the specific sequence Fibonacci noticed, e.g. it has to start 0,1. (He spotted it in various places in nature, apparently.) So is there a name for Fibonacci-like sequences?

Yes, I am still doing these in my head.

Gif

P.S. 514,229

We just passed A471151.
Interesting question: which seeds will bring up 471151 somewhere?

832040

1346269

In answer to Marjin's question:
235575 and 235576 (interesting, two consecutive numbers...)
188459 and 141346
137720 and 65237
114057 and 25796
96899 and -1668
87203 and -17421.

How's that?

H.

2,178,309

That is what you get for not being exacly enough.

471,151 and 0 or 471,150 and 1 would also work.
I was actually looking for the smallest two positive whole numbers that would somewhere have 471,151 in its series.

2,178,309

Um... this is weird, I looked at the entry yesterday, and it deffo only mentions 2 seed numbers, not that they had to begin with 0 and 1 (and this thread began only with 0)....

so, is the Fibonacci thing only the sequence that starts 0,1...
or can it be any sequence given any two seeds?

YAY the first doublepost!!!

3,524,578 to ignore the double.

5702887

OK, if you're going to start being picky, Marjin

The *smallest* *integer* solution I could find was:

307 and 753

Put those at position 1 and 2, and your target pops up at position 16. Couldn't find any lower ones than that. Interesting problem. I wonder if there are any (1) practical uses (2) lower solutions (3) actual algorithms for doing this. Anyone?

H.

I'll go take a look.


9,227,465

14,930,352

Will this do? http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibFormula.html

24,157,817

Not quit, it finds the next number, not the previous of a generalised series.

I found http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibFormulae.html
with G(n) = G(0) F(n – 1) + G(1) F(n) where G(n) = the n-th number, G(0) and G(1) the seeds and F(n) the n-th Fibonacci number.

Gives some work to do.