[seqfan] Re: Starting and Ending Digits

[Joshua Zucker]

On Fri, Jan 30, 2009 at 1:17 PM, Richard Mathar
<mathar at strw.leidenuniv.nl> wrote:
> ftaw> Date: Wed, 28 Jan 2009 18:35:54 -0500
> ftaw> From: franktaw at netscape.net
> ftaw> 1,10,20,30,40,50,60,70,80,90,100,101,11,12,2,
> ftaw> 21,13,3,31,14,4,41,15,5,51,16,6,61,17,7,71,18,

>
> [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 11, 12, 2, 21, 13, 3, 23, 31,
>
>    14, 4, 24, 34, 41, 15, 5, 25, 35, 45, 51, 16, 6, 26, 36, 46, 56, 61, 17, 7,
>
>    27, 37, 47, 57, 67, 71, 18, 8, 28, 38, 48, 58, 68, 78, 81, 19, 9, 29, 39,
>
>    49, 59, 69, 79, 89, 91, 102, 22, 32, 42, 52, 62, 72, 82, 92, 112, 120, 103,
>
>    33, 43, 53, 63, 73, 83, 93, 113, 123, 130, 104, 44, 54, 64, 74, 84, 94,
>
>    114, 124, 134, 140, 105, 55]

My own code gives
1 10 20 30 40 50 60 70 80 90 100 101 11 12 2 21 13 3 23 31 14 4 24 34
41 15 5 25 35 45 51 16 6 26 36 46 56 61 17 7 27 37 47 57 67 71 18 8 28
38 48 58 68 78 81 19 9 29 39 49 59 69 79 89 91 102 22 32 42 52 62 72
82 92 112 120 103 33 43 53 63 73 83 93 113 123 130 104 44 54 64 74 84
94 114 124 134 140 105 55 65

(written in DrScheme) so I think Richard Mathar's terms are correct,
for the original definition: *contains* last digit of previous term.

I think ftaw's sequence is defined a bit differently: *starts with*
last digit of previous term.  Well, not exactly, because some things
end in 0, and nothing starts with 0.  But after the things ending in
0, that is, starting with 101, it appears to be using that definition?
 In that case, I get

1 10 20 30 40 50 60 70 80 90 100 101 11 12 2 21 13 3 31 14 4 41 15 5
51 16 6 61 17 7 71 18 8 81 19 9 91 102 22 23 32 24 42 25 52 26 62 27
72 28 82 29 92 201 103 33 34 43 35 53 36 63 37 73 38 83 39 93 301 104
44 45 54 46 64 47 74 48 84 49 94 401 105 55 56 65 57 75 58 85 59 95
501 106 66 67 76 68 86 69 96 601 107 77 78 87 79 97 701 108 88 89

So maybe there are two sequences here?  Three sequences?  My latest
effort still doesn't seem to match (look at the term after 92, for
example).

--Joshua Zucker