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## #26 2014-09-03 04:58:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: f(f(n))

No, I did not read it.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #27 2014-09-03 05:01:31

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: f(f(n))

No, I did not read it.

Hahhahhaha, very good! Wunderbar!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #28 2014-09-03 05:05:03

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: f(f(n))

Where did Somos get those reccurences from?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #29 2014-09-03 05:08:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: f(f(n))

He is an expert in combinatorics and sequences. While I am an occasional contributor to the OEIS he is a major force. It is his knowledge of sequences that produces those. I know the technique but I lack the skill even with M. But as you should know RIPOSTP is allowed in problem solving.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #30 2014-09-03 10:08:56

bob bundy
Registered: 2010-06-20
Posts: 8,229

### Re: f(f(n))

Define a function as follows:

n ∈ [3,6]         f(n) = n + 3
n ∈ [9,18]       f(n) = n + 9
n ∈ [27,54]     f(n) = n + 27

in general:

n ∈ [3^k, 2 times 3^k]       f(n) = n + 3^k

n ∈ (6,9)         f(n) = n + 2n - 9
n ∈ (18,27)     f(n) = n + 2n - 27
n ∈ (54,81)     f9n) = n + 2n - 81

in general:

n ∈ (2 times 3^k, 3^(k+1))      f(n) = n + 2n - 3^(k+1)

f(2001) ?

As 1458 < 2001 < 2187   k = 6   and f(2001) = 2001 + (4002 - 2187) = 3816

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #31 2015-06-27 12:50:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: f(f(n))

Agnishom wrote:

Where did Somos get those reccurences from?

They come from the additive solution to the Cauchy equation, see p6 of Introduction to Functional Equations by Prasanna K. Sahoo.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #32 2015-06-27 17:30:18

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: f(f(n))

Okay. Do you know why you revived this thread?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #33 2015-06-27 18:20:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: f(f(n))

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #34 2017-05-05 02:37:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: f(f(n))

Hi;

Much time has passed and some questions were not answered. I remedy that here.

Agnishom wrote:

``````a[n_] := 3 a[n/3] /; Mod[n, 3] == 0 && n > 1;

a[n_] := 2 a[(n - 1)/3] + a[(n - 1)/3 + 1] /; (Mod[n, 3] == 1 && n > 2);

a[n_] := a[(n - 2)/3] + 2 a[(n - 2)/3 + 1] /; (Mod[n, 3] == 2 && n > 3);``````
``a[2001] /. a[1] -> 2 /. a[2] -> 3``

3816

If you want to see M in action...

``a[2001] // FullSimplify``
Agnishom wrote:

What is J-rod?

A thing that exists in Nevada. Mind you I have never had access to this creature. It will only communicate with engineer types.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #35 2017-06-04 23:49:45

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,845
Website

### Re: f(f(n))

Is J-rod a supercomputer?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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