mutually-praising pairs

[N. J. A. Sloane]

On Wed, Mar 19, 2008 at 6:15 AM, N. J. A. Sloane <njas at research.att.com> wrote:
>  But 12 and 110 are not mutually self-desribing:  110 says 1 zero, one one
>  and 0 2's, so it describes just one legal number, 10, not 12

OK, then, I think you want the sequence:
130 230 430 530 630 730 1101 1210 2020 2210 10110 11200 21200 23100
43100 53100 63100 211100 230100 311100 411100 430100 511100 530100
611100 630100 711100 1001100 2300100 3211000 4211000 4300100 5211000
5300100 6211000 6300100
but that includes the autobiographical numbers as well.

But my first idea comes from what I see as always a danger when we
view a string of digits as a code in this way: do we allow "numbers"
which are really codes to have leading zeros, or do we forbid leading
zeros?

So I was saying 12 describes 110, and 110 = 0110, and 0110 describes
12.  I guess that isn't "allowed" under the rules for this sequence
... so go with the list above instead.

Also I don't see why we should exclude "x describes x" from the seq of
numbers x such that there exists y such that x describes y and y
describes x ... but I suppose it's up to the author, not me, to decide
such things.  In which case the autobiographical numbers should be
removed from the above list.

--Joshua