[seqfan] Re: A151659

[Benoît Jubin]

A Hagen-style definition of A151659 looks a bit simpler to me:

For a given n, define an auxiliary sequence by starting at 2^n and
then taking alternatively the usigma (A034448) and the odd part
(A000265) of the previous term. This sequence is ultimately constant
equal to 1 and a(n) is defined to be its alternating product (that is,
the product of its terms taking the inverses of the terms of odd
rank).

Example: for n=3, the auxiliary sequence is 8,9,9,10,5,6,3,4,1,1,1...
so a(n)=8^{-1}.9.9^{-1}.10.5^{-1}.6.3^{-1}.4=2.

And I encourage Hagen to submit the equivalent sequence with sigma
instead of usigma: to have a well-defined sequence, you can write "and
a(n)=0 if the auxiliary sequence never reaches 1".

In general, when a sequence is known to consist only of powers of a
given number, is it desirable to also submit the corresponding
sequence of exponents?

Benoit
				

On Mon, Jun 22, 2009 at 9:22 AM, Hagen von Eitzen<hagen at von-eitzen.de> wrote:
> N. J. A. Sloane schrieb:
>> Thanks to everyone who sent comments about that sequence.
>>
>> I will take Richard Mathar's version as the official one.
>>
>> Hagen and other friends - it seems you have a different version?
>> If so, feel free to submit it as a new sequence!
>>
>>
>>  Best regards
>>                        Neil
>>
>>
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>>
>>
>>
> While I had been very confident before, it has meanwhile been indicated
> that I should prove the odd-perfect-number-conjecture before submitting.
> This may take a while ;)
>
> Hagen
>
>
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