mutually-praising pairs

[Martin Fuller]

I have two complete versions of the sequence depending on whether the
numbers are allowed to have more than 10 digits, e.g. 73100 <->
21010001000. Allowing larger numbers also allows 3 more
autobiographical numbers.  Is this a new sequence or an extension to
A046043?

Full sequence of autobiographical numbers including greater than 10^10.
1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000,
72100001000, 821000001000, 9210000001000

Full sequence of mutually-praising pairs, excluding autobiographical
numbers. Version 1: both numbers must have at most 10 digits.
130, 230, 430, 530, 630, 730, 1101, 2210, 10110, 11200, 23100, 43100,
53100, 63100, 211100, 230100, 311100, 411100, 430100, 511100, 530100,
611100, 630100, 711100, 1001100, 2300100, 4211000, 4300100, 5211000,
5300100, 6211000, 6300100, 10010100, 21011000, 23000100, 31011000,
32101000, 41011000, 43000100, 51011000, 52101000, 53000100, 61011000,
62101000, 63000100, 71011000, 100100100, 210101000, 230000100,
310101000, 321001000, 410101000, 421001000, 430000100, 510101000,
530000100, 610101000, 621001000, 630000100, 710101000, 1001000100,
2101001000, 2300000100, 3101001000, 3210001000, 4101001000, 4210001000,
4300000100, 5101001000, 5210001000, 5300000100, 6101001000, 6300000100,
7101001000

Full sequence of mutually-praising pairs, excluding autobiographical
numbers. Version 2: allowing more than 10 digits:
130, 230, 430, 530, 630, 730, 830, 930, 1101, 2210, 10110, 11200,
23100, 43100, 53100, 63100, 73100, 83100, 93100, 211100, 230100,
311100, 411100, 430100, 511100, 530100, 611100, 630100, 711100, 730100,
811100, 830100, 911100, 930100, 1001100, 2300100, 4211000, 4300100,
5211000, 5300100, 6211000, 6300100, 7211000, 7300100, 8211000, 8300100,
9211000, 9300100, 10010100, 21011000, 23000100, 31011000, 32101000,
41011000, 43000100, 51011000, 52101000, 53000100, 61011000, 62101000,
63000100, 71011000, 72101000, 73000100, 81011000, 82101000, 83000100,
91011000, 92101000, 93000100, 100100100, 210101000, 230000100,
310101000, 321001000, 410101000, 421001000, 430000100, 510101000,
530000100, 610101000, 621001000, 630000100, 710101000, 721001000,
730000100, 810101000, 821001000, 830000100, 910101000, 921001000,
930000100, 1001000100, 2101001000, 2300000100, 3101001000, 3210001000,
4101001000, 4210001000, 4300000100, 5101001000, 5210001000, 5300000100,
6101001000, 6300000100, 7101001000, 7210001000, 7300000100, 8101001000,
8210001000, 8300000100, 9101001000, 9210001000, 9300000100,
10010000100, 21010001000, 23000000100, 31010001000, 32100001000,
41010001000, 42100001000, 43000000100, 51010001000, 52100001000,
53000000100, 61010001000, 62100001000, 63000000100, 71010001000,
73000000100, 81010001000, 82100001000, 83000000100, 91010001000,
92100001000, 93000000100, 100100000100, 210100001000, 230000000100,
310100001000, 321000001000, 410100001000, 421000001000, 430000000100,
510100001000, 521000001000, 530000000100, 610100001000, 621000001000,
630000000100, 710100001000, 721000001000, 730000000100, 810100001000,
830000000100, 910100001000, 921000001000, 930000000100, 2101000001000,
3101000001000, 3210000001000, 4101000001000, 4210000001000,
5101000001000, 5210000001000, 6101000001000, 6210000001000,
7101000001000, 7210000001000, 8101000001000, 8210000001000,
9101000001000

Martin Fuller

--- Joshua Zucker <joshua.zucker at gmail.com> wrote:

> 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.
> 
...
> --Joshua
>