Question related to sequence A071267

[Diana Mecum]

Joshua,

Yes, I will double check that your and my terms agree. I will submit the
corrected list, as that was my purpose in studying the list in the first
place.

Thanks for your time.

Diana M.


On 7/11/07, Joshua Zucker <joshua.zucker at gmail.com> wrote:
>
> Hi Diana and all,
> Murthy's sequences often have errors.  Here, among other problems, the
> definition is "numbers which ..." but then shouldn't they be SORTED?
>
> I don't quite agree with your list, either, though.  Here's what I
> think, based purely on brute-force with a computer, using as "seeds"
> all the numbers up to 100000:
>
> 1 2 3 4 5 6 7 8 9 11 22 33 44 55 66 77 88 99 110 111 121 132 143 154
> 165 176 187 222 333 444 555 666 777 888 999 1110 1111 1221 1332 1443
> 1554 1665 1776 1887 1998 2109 2220 2222 2331 2442 2553 2664 2775 2886
> 3108 3330 3333 3552 3774 3996 4218 4440 4444 4662 4884 5106 5328 5555
> 6666 7777 8888 9999 11110 11111 12221 13332 14443 15554 16665 17776
> 18887 19998 21109 22220 22222 23331 24442 25553 26664 27775 28886
> 29997
>
> which leaves me wondering, for instance, why I got 29997 but not 2997
> in there.  But now I see it's a nice little bit of combinatorics: 108
> goes to 1998 (six permutations, so effectively each spot is
> (1+0+8+1+0+8) so we get 1800 + 180 + 18), while 1008 goes to 29997
> (twelve permutations, so each spot is (1+0+0+8+1+0+0+8+1+0+0+8) so we
> get 27000 + 2700 + 270 + 27).
>
> So I think my above list of terms are correct.  Differences from your
> list, Diana, are that I have 333 and 1111 and 2222 and 2331 and 2553
> and 2775 and 3333 which are missing from your list.  (2331 for example
> comes from 399 -> 399 + 939 + 993, and any list of identical digits
> maps to itself, so 333 -> 333.)
>
> Diana, would you verify that you agree with my list of terms and then
> if you do please submit the corrected terms for this sequence?
>
> Thanks,
> --Joshua Zucker
>
>
> On 7/11/07, Diana Mecum <diana.mecum at gmail.com> wrote:
> > Sequence Fans,
> >
> > I am looking at sequence A071267.
> >
> > %I A071267
> > %S A071267
> > 2,4,6,8,10,11,12,14,16,18,22,33,44,55,66,77,88,99,101,110,121,132,143,
> > %T A071267 154,165,176,187,198,111,222,666,888,1110
> > %N A071267 Numbers which can be expressed as the sum of all distinct
> digit
> > permutations of
> >                some number k.
> > %C A071267 222 can be expressed so in two different ways i.e. 222= 200
> +020
> > + 002 as well as
> >                222= 101 +110 +011. Question: find a number which can be
> so
> > expressed
> >                 in n different ways.
> > %e A071267 1110 is a member as a sum of all distinct permutations of
> 104.
> > i.e. 104,140,410,
> >                401,014,041.
> > %Y A071267 Sequence in context: A081472 A097660 A067030 this_sequence
> > A072427 A050420 A096922
> > %Y A071267 Adjacent sequences: A071264 A071265 A071266 this_sequence
> A071268
> > A071269 A071270
> > %K A071267 base,more,nonn
> > %O A071267 1,1
> > %A A071267 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 01 2002
> >
> > When I try to follow the rule for generating the sequence numbers, I get
> the
> > following list;
> >
> > 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 111,
> > 121, 132, 143, 154, 165,
> >  176, 187, 222, 444, 555, 666, 777, 888, 999, 1110, 1221, 1332, 1443,
> 1554,
> > 1665, 1776, 1887,
> >  1998, 2109, 2220, 2442, 2664, 2886, 3108, 3330, 3552, 3774, 3996
> >
> > Can someone explain why my list differs from the original? I am not
> > understanding the hypothesis to generate the original list.
> >
> > Diana M.
> >
> > --
> > "God made the integers, all else is the work of man."
> > L. Kronecker, Jahresber. DMV 2, S. 19.
>



-- 
"God made the integers, all else is the work of man."
L. Kronecker, Jahresber. DMV 2, S. 19.
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