# [seqfan] Re: Numbers impossible to produce

Peter Pein petsie at dordos.net
Thu Apr 14 13:59:57 CEST 2011

```Am 14.04.2011 13:41, schrieb Eric Angelini:
> Hello SeqFans,
>
> The integer 126 produces 38 like this:
>
>   1 2 6
>    3 8
>
> A digit on the base line is the addition
> of the two closest digits above it.
>
> What does the integer 176 produce?
> We decide that if the sum a+b of the said
> digits is greater than 9, than we subtract
> a from b (or b from a if a>  b):
>
>   1 7 6
>    8 1
>
> So, we managed to produce 38 and 81; but
> what could be the smallest number that
> would be impossible to produce, according
> to the above rule?
>
> Best,
> É.
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

here are the least three-digit numbers which produce 0,1,...,99:

{555, 556, 557, 558, 559, 550, 551, 552, 553, 554, 100, 101, 102, \
103, 104, 105, 106, 107, 108, 109, 200, 110, 111, 112, 113, 114, 115, \
116, 117, 118, 300, 210, 120, 121, 122, 123, 124, 125, 126, 127, 377, \
310, 220, 130, 131, 132, 133, 134, 135, 136, 388, 387, 146, 147, 140, \
141, 142, 143, 144, 145, 155, 156, 157, 158, 159, 150, 151, 152, 153, \
154, 166, 165, 164, 169, 259, 250, 160, 161, 162, 163, 177, 176, 175, \
174, 173, 194, 193, 170, 171, 172, 188, 187, 186, 185, 184, 183, 182, \
270, 180, 181}

Cheers,
Peter

```