branching in p-morphics

David Wilson davidwwilson at
Tue Sep 24 12:35:37 CEST 2002

----- Original Message -----
From: "ZAKIRS" <zfseidov at>
To: "'David Wilson'" <davidwwilson at>; "???? ?????? - ?"?/Zakir
Seidov Ph.D." <zfseidov at>; "Sequence Fanatics"
<seqfan at>
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
>  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
a finite number of automorphics.

I rechecked my work, and found that for d >= 3, there are exactly 15
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


leaving the 11 you included in A074194.

By way of explanation of my earlier mistake, I had inferred from your
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
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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