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Allo PEg, nice of you to drop in.

Your definition of intelligent is what I'd consider as clever. How would you define smart and clever?

Funny, eh, the English language. You can have ten people say the same thing and mean something slightly different in each case.

I'd say that smart was: quick to comprehend, with an implication of sassiness or newness to it. I'd define clever as witty, with overtones of foxiness and an implication that rule bending might be allowable.

All those words have to do with how much good stuff there is in the Central Processing Unit, but some have more to do with RAM than mother board, and others more to do with software . . .

It's nice to be able to pop in, thanks, bel! You're right about English. Some of us treat it as Humpty Dumpty does in Alice. Lack of shared references can keep two people who share the same language from communicating well, can't it?

Hey, Peg, good to meet you (again)!

Now, hwa?

OP Hmm.. I wonder if the whole culture debate is the reason that the SAT was recently changed.

[insert signature here]

What is the next number in this series:

1, 2, 9, 262144,____

What is the next number in this series: Is there one that makes some sort of logical sense?

Quote:

What is the next number in this series:

1, 2, 9, 262144,____

I don't know how the 1 was derived, perhaps by defining it, but the second number is 2 to the power of the number preceding it; the third number is 3 to the power of the number preceding it; the fourth number is 4 to the power of the number preceding it; so the fifth number would be 5 to the power of the number preceding it. Deriving the actual number is trivial, so I will leave that up to the reader. I can give you a big hint, though. It ends in 25.

TEd

Electronic hard wired color displays are designated as "pallettes".

Pallette1lets us see 114 color shades.

Pallette2lets us see 543 color shades.

Pallette9lets us see262,144different shades of colors, the most available.

So the answer to the so calledFaldage Sequenceis "0" ( as in "none") because there are no further shady mechanisms in the electronic marketplace today.1,(114)2,(543)9,(262,144)0

The closest I've come up with is 6.206e183230

The recursion is, as TEd sussed, N^=N to the (N-1)^. I haven't decided how to define the base but it doesn't quite matter. It could be 0^=0, 0^=1 or 1^=1. I kinda like the first version just because it seems the elegantest.

You have artistic license when it comes to defining the first numbers in a sequence. Sometimes by playing around with them you get cool results.

One of the interesting things about the Fibonacci sequence is that the ratios of successive numbers such 8/5, 13/8, 21/13, etc, approach the famous irrational number known as Phi , associated with the Golden Ratio. But what's even more interesting, is that no matter how you define the first two numbers in the Fibonacci sequence -- suppose your sequence begins 7, 8, 15, 23, 38... -- the ratios of consecutive numbers will still converge on this value 1.61803399. You can even begin with 0 and 7, ensuring a Fibonacci-esque sequence whose members are all multiples of seven, and the ratios of successive numbers in the list will converge to Phi.

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