## Is this true?

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• Hi! Let S(C,B) be the sum of the digits of C in base B Let mod(x,y) be the remainder of x/y (integer division) I´ve just found that: Sum (n=1 to oo) (
Message 1 of 9 , Feb 14, 2002
Hi!

Let S(C,B) be the sum of the digits of C in base B
Let mod(x,y) be the remainder of x/y (integer division)

I´ve just found that:

Sum (n=1 to oo) ( mod(C,B^n) / B^n ) = S(C,B)/(B-1)

I cannot prove it because I´m not too smart ;-)
Does it sound familiar to anybody? Maybe it´s obvious.

Thanks

Néstor
• Hi! ... Write C in base B as (c_{m-1} c_{m-2} ... c_ 1 c_0)_B . For n = m we have mod(C, B^n) = C but for n
Message 2 of 9 , Feb 18, 2002
Hi!

Robin Chapman wrote this on Sci.math. I think it is correct:

---------------------------------------------------------

Write C in base B as (c_{m-1} c_{m-2} ... c_ 1 c_0)_B .
For n >= m we have mod(C, B^n) = C but for n < m
we have mod(C, B^n) = (c_{n-1} c_{n-2} ... c_ 1 c_0)_B
= c_0 + c_1 B + ... + c_{n-1} B^{n-1}
The sum is
c_0/B
+ (c_0/B^2 + c_1/B)
+ (c_0/B^3 + c_1/B^2 + c_2/B)
+ ....
+ (c_0/B^m + c_1/B^{m-1} + ... + c_{m-1}/B)
+ ...
+ (c_0/B^n + c_1/B^{n-1} + ... + c_{m-1}/B^{m-m+1})
+ ...

= (c_0 + c_1 + ... + c_{m-1})(1/B + 1/B^2 + ...)

= (c_0 + c_1 + ... + c_{m-1})/(B-1).

--------------------------------------------------------

Thanks

Néstor
• ... If Robin wrote it, then that s the default opinion you should start with. ... The sum of what? ... Why are you dividing by B? ... and by B^2? ... Certainly
Message 3 of 9 , Feb 18, 2002
On Mon, 18 February 2002, "cashogor" wrote:
> Hi!
>
> Robin Chapman wrote this on Sci.math. I think it is correct:

If Robin wrote it, then that's the default opinion you should start with.

> Write C in base B as (c_{m-1} c_{m-2} ... c_ 1 c_0)_B .
> For n >= m we have mod(C, B^n) = C but for n < m
> we have mod(C, B^n) = (c_{n-1} c_{n-2} ... c_ 1 c_0)_B
> = c_0 + c_1 B + ... + c_{n-1} B^{n-1}
> The sum is

The sum of what?

> c_0/B

Why are you dividing by B?

> + (c_0/B^2 + c_1/B)

and by B^2?

> + (c_0/B^3 + c_1/B^2 + c_2/B)
> + ....
> + (c_0/B^m + c_1/B^{m-1} + ... + c_{m-1}/B)
> + ...
> + (c_0/B^n + c_1/B^{n-1} + ... + c_{m-1}/B^{m-m+1})
> + ...
>
> = (c_0 + c_1 + ... + c_{m-1})(1/B + 1/B^2 + ...)
>
> = (c_0 + c_1 + ... + c_{m-1})/(B-1).

Certainly the right hand side is correctly manipulated, although the final step does require more rigour - it's not an infinite sum - but to be honest I can't see what the question, to which this is an answer, is.

Phil

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They've taken Wolfram's money - _don't_ give them yours.
http://mathworld.wolfram.com/erics_commentary.html

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• Hi Phil! ... Let S(C,B) be the sum of the digits of C in base B Let mod(x,y) be the remainder of x/y (integer division) I´ve just found that: Sum (n=1 to oo)
Message 4 of 9 , Feb 18, 2002
Hi Phil!

I posted a message recently that said:

---------------------------------------------------

Let S(C,B) be the sum of the digits of C in base B
Let mod(x,y) be the remainder of x/y (integer division)

I´ve just found that:

Sum (n=1 to oo) ( mod(C,B^n) / B^n ) = S(C,B)/(B-1)

I cannot prove it because I´m not too smart ;-)
Does it sound familiar to anybody? Maybe it´s obvious.

-----------------------------------------------------

And that´s what Robin seems to have proved.

Néstor.
• Point (1): There is a pattern in compound numbers. This implies that compound numbers have a function. Point (2): There is a relationship between compound
Message 5 of 9 , Sep 2, 2009
Point (1): There is a pattern in compound numbers. This implies that compound numbers have a function.

Point (2): There is a relationship between compound numbers and squares of primes. This implies that squares of primes have a function dependent on the function of compounds.

Point (3): The pattern in prime numbers is related to "Point 2". This implies that prime numbers have a function.

Regards.
• Why do I make very silly mistakes even when I am serious, the question should read: Point (1): There is a pattern in composite numbers. This implies that
Message 6 of 9 , Sep 2, 2009
Why do I make very silly mistakes even when I am serious, the question should read:

Point (1): There is a pattern in composite numbers. This implies that composite numbers have a function.

Point (2): There is a relationship between composite numbers and squares of primes. This implies that squares of primes have a function dependent on the function of composites.

Point (3): The pattern in prime numbers is related to "Point 2". This implies that prime numbers have a function.

[Non-text portions of this message have been removed]
• I am not sure what your point is, but it seems to center on the Urban myths that there are no functions which describe the primes. There are many (none
Message 7 of 9 , Sep 2, 2009
I am not sure what your point is, but it seems to center on the Urban
myths that there are no functions which describe the primes. There are
many (none particularly useful, but dozens have been published). For
subsets of the primes, my favorite is Mills'

The primes are a pattern.

-----Original Message-----
On Behalf Of Billy Hamathi
Sent: Wednesday, September 02, 2009 4:50 AM
Subject: [PrimeNumbers] Re: Is this true?

Why do I make very silly mistakes even when I am serious, the question

Point (1): There is a pattern in composite numbers. This implies that
composite numbers have a function.

Point (2): There is a relationship between composite numbers and squares
of primes. This implies that squares of primes have a function dependent
on the function of composites.

Point (3): The pattern in prime numbers is related to "Point 2". This
implies that prime numbers have a function.

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

------------------------------------

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The Prime Pages : http://www.primepages.org/

• Thanks Chris, but could you answer me without answering what my question could imply? Is it true? ... From: Chris Caldwell Subject: RE:
Message 8 of 9 , Sep 2, 2009
Thanks Chris, but could you answer me without answering what my question could imply? Is it true?

--- On Wed, 2/9/09, Chris Caldwell <caldwell@...> wrote:

From: Chris Caldwell <caldwell@...>
Subject: RE: [PrimeNumbers] Re: Is this true?
Date: Wednesday, 2 September, 2009, 4:35 PM

I am not sure what your point is, but it seems to center on the Urban
myths that there are no functions which describe the primes. There are
many (none particularly useful, but dozens have been published). For
subsets of the primes, my favorite is Mills'

The primes are a pattern.

-----Original Message-----
On Behalf Of Billy Hamathi
Sent: Wednesday, September 02, 2009 4:50 AM
Subject: [PrimeNumbers] Re: Is this true?

Why do I make very silly mistakes even when I am serious, the question

Point (1): There is a pattern in composite numbers. This implies that
composite numbers have a function.

Point (2): There is a relationship between composite numbers and squares
of primes. This implies that squares of primes have a function dependent
on the function of composites.

Point (3): The pattern in prime numbers is related to "Point 2". This
implies that prime numbers have a function.

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

------------ --------- --------- ------

Unsubscribe by an email to: primenumbers- unsubscribe@ yahoogroups. com
The Prime Pages : http://www.primepag es.org/

[Non-text portions of this message have been removed]
• ... Do you have time to elaborate a bit on that ? Though I think that I know what you are talking about, I would like to read your own version, with examples
Message 9 of 9 , Sep 2, 2009
Chris Caldwell wrote:
> I am not sure what your point is, but it seems to center on the Urban
> myths that there are no functions which describe the primes. There are
> many (none particularly useful, but dozens have been published). For
> subsets of the primes, my favorite is Mills'
>
> The primes are a pattern.

Do you have time to elaborate a bit on that ?
Though I think that I know what you are talking