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

F(102) = 927,372,692,193,078,999,176

Congratulations master B, you gave us F(100)

F(103) = 1,500,520,536,203,896,083,277

Incidentally, F(103)/F(102) = 1.6180339887..., which is indistinguishable from the Golden Mean, at least on my calculator!

F(104) = 2,427,893,228,399,975,082,453

Actually that is hardly remarkable.

There is also a formula that, given one Fibonacci number, returns the next Fibonacci number directly, calculating it in terms only of the previous value (ie not needing the value before as well).

F(n+1) = round( F(n) Phi )

with Phi the Golden Section number.

3,928,413,764,603,871,165,720

I still find pen and paper easier.

B

http://pauillac.inria.fr/algo/bsolve/constant/gold/gold.html

"We claim that the Golden mean is intricately related to Fibonacci's sequence"

Fascinating stuff.

Nice link, Jim - I'm sure it wouldn't have taken us long to come up with the proof

6,356,306,993,003,846,248,173

I'm not sure if the related

http://pauillac.inria.fr/algo/bsolve/constant/sofa/sofa.html

is a wind-up or not.

B

927,372,692,193,078,999,176

Keep up Bagpuss, that was a while ago.

B

F(107) = 10,284,720,757,613,717,413,913

I have not checked the previous ones this time, but yours should be
F(106) = 6356306993006846248183 Master B!

Other interesting links can be found way back in the b'log, post 39 and 40

Look, smart-ar*e, I've contributed more bloody posts to this thread than anyone else - I'm bound to get a couple wrong

At least I can keep up, unlike Bagpuss (now demonstrated twice)

16,641,027,750,620,563,662,096

B

I know you posted a lot, but we try to get the correct numbers, not the most posts.
F(109) = 26,925,748,508,234,281,076,009

43,566,776,258,854,844,738,105

Damn it, it's _MY_ thread and if Master B posted the most he is the winner!

Liam.

F(111) = 70,492,524,767,089,125,814,114

Will this ever end?

114,059,301,025,943,970,552,219

By definition, no.

B

184,551,825,793,033,096,366,333

Ah...oh dear

F(113)=184,551,825,793,033,096,366,333

That one had refreshingly few carry-digits. I'm working from left to right, w/out paper, so it's nice when there aren't many.

Simulpost! At least we got the same number.

F(114)=298,611,126,818,977,066,918,552

F(115) = 483,162,952,612,010,163,284,885

F(116)=781,774,079,430,987,230,103,437

Am I on the right page?

Master B, I doubt the sofa thing is a wind-up. It's a perfectly reasonable geometric question that's just been given an odd name by some mathematician. The days when we named everything in Greek or Latin are long gone - yesterday I was reading a paper that discussed forks and noodles.

F(117)=1,264,937,032,042,997,393,388,322

This is more fun than it looks, I'm finding. Working out the most efficient way to add long numbers without paper and then doublecheck one's work is pretty interesting. I tried a right-to-left, base 1000 doublecheck - very satisfactory!