branching in p-morphics
David Wilson
davidwwilson at attbi.com
Tue Sep 24 12:35:37 CEST 2002
----- Original Message -----
From: "ZAKIRS" <zfseidov at ycariel.yosh.ac.il>
To: "'David Wilson'" <davidwwilson at attbi.com>; "???? ?????? - ?"?/Zakir
Seidov Ph.D." <zfseidov at ycariel.yosh.ac.il>; "Sequence Fanatics"
<seqfan at ext.jussieu.fr>
Sent: Tuesday, September 24, 2002 4:38 AM
Subject: RE: branching in p-morphics
> David, i'm not sure that i understand these your words about
"infinitude".
> i claim in A074194 that there are only 11 3-morphics for number of digits
> >=4., zak.
Yes, disregard my last post on this subject. You are in fact right, there
are
a finite number of automorphics.
I rechecked my work, and found that for d >= 3, there are exactly 15
trimorphic
residues mod 10^d. These residues correspond to d-digit trimorphs,
some of them have leading zeroes. In particular, for d >= 2, the trimorphic
residues 0 and 1 lead to d-digit trimorphs 000...000 and 000...001, which
will always be omitted because of leading zeroes. This means there can
be at most 13 d-digit automorphs for d >= 3.
In the case of A074194 (35-digit automorphs), two other residues happened
to have leading zeros, and were omitted as well. These were
09004106619977392256259918212890624
09004106619977392256259918212890625
leaving the 11 you included in A074194.
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By way of explanation of my earlier mistake, I had inferred from your
earlier
mail that the number of d-digit trimorphs was unbounded with increasing d,
and that you were experiencing the branching effect you mentioned. This
colored my analysis of the problem, so I failed to see that the d-digit
trimorphs
were in fact bounded in number. Sorry for the mistake.
It often happens that things we know blind us to things that are true.
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