- Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is nth term of

fibonacci sequence. The first few terms are 2,3,7,13,25,73...........

Notice that all terms except 25 are primes. I think that other terms

of the sequence are even so I think there will be no more primes. What

do you think? - On Friday 04 March 2005 15:33, you wrote:
> Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is nth term of

There seems to be a definite pattern to the parity of n*f(n). Try to work from

> fibonacci sequence. The first few terms are 2,3,7,13,25,73...........

> Notice that all terms except 25 are primes. I think that other terms

> of the sequence are even so I think there will be no more primes. What

> do you think?

there and see what you can prove about your sequence.

Décio

[Non-text portions of this message have been removed] - For...

f( 1): 1

f( 2): 1

f( 3): 2

f( 4): 3

f( 5): 5

f( 6): 8

f( 7): 13

f( 8): 21

f( 9): 34

f(10): 55

I get...

a( 1): 2

a( 2): 3

a( 3): 5

a( 4): 11

a( 5): 23

a( 6): 48

a( 7): 96

a( 8): 187

a( 9): 355

a(10): 661

.....

--- mcnamara_gio <mcnamara_gio@...> wrote:>

__________________________________

> Define sequence a(n+1)=n*f(n)+a(n), a(1)=2, f(n) is

> nth term of

> fibonacci sequence. The first few terms are

> 2,3,7,13,25,73...........

> Notice that all terms except 25 are primes. I think

> that other terms

> of the sequence are even so I think there will be no

> more primes. What

> do you think?

>

>

>

>

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