Math Is Fun Forum
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#26 2014-09-03 04:58:42
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
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
- Administrator
- Registered: 2010-06-20
- Posts: 10,627
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
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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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))
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
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))
Some guy that has your username asked a question that I was unable to give a good answer to before. The book I was reading for another functional problem had a good answer.
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.
your code, please?
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] -> 33816
If you want to see M in action...
a[2001] // FullSimplifyWhat 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
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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