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## Question

I cannot tell a lie, although you may think I am with these sequences:

1) 2, 3, 5, 13, 89...

2) 3, 4, 5, 7, 11...

3) 1, 2, 3, 8, 24, 90...

What are the next numbers in these sequences?

All of them have something in common...really...I'm not lying. It may help to do them in the order that I have written them

I don't really expect you to go very much further with the sequence without the use of a computer of some sort...

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The second number in the fibonachi sequence is 3

The third number in the fibonachi sequence is 5

The fith number is 13, etc, etc,

That is the first sequence, right?

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1) 2, 3, 5, 13, 89, 144 - skip first 3 then take 3, skip 1 then take 1

2) 3, 4, 5, 7, 11, 12 - the Fibonacci numbers (F3, F4..)of the above sequence

3) not sure yet

F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

Edited by Snowman63
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The second number in the fibonachi sequence is 3

The third number in the fibonachi sequence is 5

The fith number is 13, etc, etc,

That is the first sequence, right?

That's not right.

The Fibonacci sequence is:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

2nd Fibonacci number is 1

1st Fibonacci number is 1

1st Fibonacci number is 1....

So that doesn't work. Even if you throw out the two 1's starting the sequence:

2nd Fibonacci number is 3

3rd Fibonacci number is 5

5th Fibonacci number is 13

13th Fibonacci number is 610 (not 89)

Fibonacci Primes:

2, 3, 5, 13, 89, 233, 1597, 28657...

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I agree with dwilly

The primes make more sense so:

1- 233

2- 13

3- still working on it

Edited by Snowman63
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My attempt

1st one

prime fibonnaci nos. nxt is 223

2nd one

3, 4, 5, 7, 11,18

1st order diff 1,1,2,4,7

2nd order diff 0,1,2,3

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Fibonacci Primes:

2, 3, 5, 13, 89, 233, 1597, 28657...

You are correct dwilly on the first sequence, and snowman is correct on the second sequence (assuming you know WHY it is the answer you gave)...

So, yes, the first sequence is fibonacci primes, the second is the index of those primes in the fibonacci sequence.

The third sequence isn't quite as tightly coupled to the other two...but still involves fibonacci...more math involved here...

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Again, #3 has something in common with numbers 1 and 2...and the formula for this sequence can be expressed in a simple fraction:

X1/X2

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