A023153 through A023161

[Jonathan Post]

"almost multiplicative" -- interesting notion.  What other "almost
multiplicative" are there in OEIS masquerading as multiplicative (i'm
guessing that the amazing Tony Noe is searching), and what are but with no
keyword on that? Can "almost multiplicative" be axiomatizeed, or is it just
a subjective interpretation of "almost"? What pattens are there in "almost
multiplicative" -- new sequences on where multiplicativity breaks down?

-- Jonathan Vos Post

On 11/14/06, David Wilson <davidwwilson at comcast.net> wrote:
>
> Tony Noe has found that A023153 through A023161 are not multiplicative as
> I
> had marked them.
>
> At the time, I was convinced that in sequence {s_k(n) = k^(2^n)}, a cycle
> of
> period x (mod a) and a cycle of period y (mod b) implied a unique cycle of
> period xy (mod ab). However, if gcd(x, y) > 1, the cycles (mod a) and (mod
> b) can align in more than one way, producing more than one cycle (mod ab).
> For example, the cycle (2,4) (mod 7) and the cycle (4,7) (mod 9) produce
> two
> cycles (4,16) and (25,58) (mod 63). This means that sometimes f(ab) >
> f(a)f(b).
>
> This problem affects A023153 through A023161, and Tony Noe has shown that
> indeed none of these are multiplicative.
>
> NJAS: Please remove the "mult" keyword and any comments related to
> multiplicativity from A023153-A023161.
>
> Tony: Since these sequences are almost multiplicative, but are not, and
> you
> seem to be investigating these sequences, could you please add lines such
> as
>
> %C A023153 Not multiplicative: a(63) = 10, but a(7)*a(9) = 3*3 = 9.
>
> Thanks for spotting my error, Tony. Seems I have been bitten by the dragon
> I
> released.
>
> ----- Original Message -----
> From: "T. D. Noe" <noe at sspectra.com>
> To: <davidwwilson at comcast.net>
> Sent: Tuesday, November 14, 2006 2:06 AM
> Subject: Question about A023161
>
>
> > David, according to my calculations, this sequence fails to be
> > multiplicative at a(667).
> >
> > Best regards,
> >
> > Tony
> >
> >
> > --
> > No virus found in this incoming message.
> > Checked by AVG Free Edition.
> > Version: 7.5.430 / Virus Database: 268.14.5/533 - Release Date:
> 11/13/2006
> > 8:56 PM
> >
> >
>
>
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