Dimitroff's Puzzle

[David Wasserman]

>
>http://www.research.att.com/projects/OEIS?Anum=A095026
>1,
>3,1,
>5,2,2,
>8,2,4,2,
>9,4,4,4,4,
>15,2,6,5,6,2,
>13,6,6,6,6,6,6,
>20,4,8,4,12,4,8,4,
>21,6,6,12,6,6,12,6,6,
>27,4,12,4,12,9,12,4,12,4,
>... could probably be extended ...
>21,......
 

I have submitted an extension, with enough terms to fill %S, %T, and %U.  The first 50 rows are at the end of this message.

BTW, is it really appropriate to put the keyword "base" on this sequence?  I thought that meant that we'd get different values if we used some base other than 10.  For example, if we wrote numbers in base 5, this sequence would begin
1,
3,1,
10,2,2,
13,2,4,2,
etc.,  which looks different, but it represents the same values.
In constrast, consider this sequence:

%I A061917
%S A061917 0,1,2,3,4,5,6,7,8,9,10,11,20,22,30,33,40,44,50,55,60,66,70,77,80,
%T A061917 88,90,99,100,101,110,111,200,202,212,220,222,232,242,252,262,272,
%U A061917 282,292,300,303,313,323,330,333,343,353,363,373,383,393,400,404
%N A061917 Either a palindrome or becomes a palindrome if trailing 0's are omitted.
%Y A061917 Cf. A002113, A057890, A062019.
%Y A061917 Sequence in context: A009996 A032907 A061362 this_sequence A055933 A068637 A064222
%Y A061917 Adjacent sequences: A061914 A061915 A061916 this_sequence A061918 A061919 A061920
%K A061917 nonn,base,easy,nice
%O A061917 0,3
%A A061917 njas, Jun 27 2001

If we used base 5, we would get
0,1,2,3,4,10,11,20,22,30,33,...
which doesn't represent the same values.

 - David


1:  1,
2:  3,1,
3:  5,2,2,
4:  8,2,4,2,
5:  9,4,4,4,4,
6:  15,2,6,5,6,2,
7:  13,6,6,6,6,6,6,
8:  20,4,8,4,12,4,8,4,
9:  21,6,6,12,6,6,12,6,6,
10:  27,4,12,4,12,9,12,4,12,4,
11:  21,10,10,10,10,10,10,10,10,10,10,
12:  40,4,8,10,16,4,20,4,16,10,8,4,
13:  25,12,12,12,12,12,12,12,12,12,12,12,12,
14:  39,6,18,6,18,6,18,13,18,6,18,6,18,6,
15:  45,8,8,20,8,18,20,8,8,20,18,8,20,8,8,
16:  48,8,16,8,24,8,16,8,32,8,16,8,24,8,16,8,
17:  33,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
18:  63,6,18,12,18,6,36,6,18,21,18,6,36,6,18,12,18,6,
19:  37,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
20:  72,8,16,8,32,18,16,8,32,8,36,8,32,8,16,18,32,8,16,8,
21:  65,12,12,30,12,12,30,26,12,30,12,12,30,12,26,30,12,12,30,12,12,
22:  63,10,30,10,30,10,30,10,30,10,30,21,30,10,30,10,30,10,30,10,30,10,
23:  45,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,
24:  100,8,16,20,24,8,40,8,40,20,16,8,60,8,16,20,40,8,40,8,24,20,16,8,
25:  65,20,20,20,20,40,20,20,20,20,40,20,20,20,20,40,20,20,20,20,40,20,20,20,20,
26:  75,12,36,12,36,12,36,12,36,12,36,12,36,25,36,12,36,12,36,12,36,12,36,12,36,12,
27:  81,18,18,36,18,18,36,18,18,54,18,18,36,18,18,36,18,18,54,18,18,36,18,18,36,18,18,
28:  104,12,24,12,48,12,24,26,48,12,24,12,48,12,52,12,48,12,24,12,48,26,24,12,48,12,24,12,
29:  57,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,28,
30:  135,8,24,20,24,18,60,8,24,20,54,8,60,8,24,45,24,8,60,8,54,20,24,8,60,18,24,20,24,8,
31:  61,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,
32:  112,16,32,16,48,16,32,16,64,16,32,16,48,16,32,16,80,16,32,16,48,16,32,16,64,16,32,16,48,16,32,16,
33:  105,20,20,50,20,20,50,20,20,50,20,42,50,20,20,50,20,20,50,20,20,50,42,20,50,20,20,50,20,20,50,20,20,
34:  99,16,48,16,48,16,48,16,48,16,48,16,48,16,48,16,48,33,48,16,48,16,48,16,48,16,48,16,48,16,48,16,48,16,
35:  117,24,24,24,24,54,24,52,24,24,54,24,24,24,52,54,24,24,24,24,54,52,24,24,24,54,24,24,52,24,54,24,24,24,24,
36:  168,12,24,24,48,12,48,12,48,42,24,12,96,12,24,24,48,12,84,12,48,24,24,12,96,12,24,42,48,12,48,12,48,24,24,12,
37:  73,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,
38:  111,18,54,18,54,18,54,18,54,18,54,18,54,18,54,18,54,18,54,37,54,18,54,18,54,18,54,18,54,18,54,18,54,18,54,18,54,18,
39:  125,24,24,60,24,24,60,24,24,60,24,24,60,50,24,60,24,24,60,24,24,60,24,24,60,24,50,60,24,24,60,24,24,60,24,24,60,24,24,
40:  180,16,32,16,48,36,32,16,80,16,72,16,48,16,32,36,80,16,32,16,108,16,32,16,80,36,32,16,48,16,72,16,80,16,32,36,48,16,32,16,
41:  81,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,40,
42:  195,12,36,30,36,12,90,26,36,30,36,12,90,12,78,30,36,12,90,12,36,65,36,12,90,12,36,30,78,12,90,12,36,30,36,26,90,12,36,30,36,12,
43:  85,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,
44:  168,20,40,20,80,20,40,20,80,20,40,42,80,20,40,20,80,20,40,20,80,20,84,20,80,20,40,20,80,20,40,20,80,42,40,20,80,20,40,20,80,20,40,20,
45:  189,24,24,48,24,54,48,24,24,84,54,24,48,24,24,108,24,24,84,24,54,48,24,24,48,54,24,84,24,24,108,24,24,48,24,54,84,24,24,48,54,24,48,24,24,
46:  135,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,45,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,66,22,
47:  93,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,
48:  240,16,32,40,48,16,80,16,64,40,32,16,120,16,32,40,96,16,80,16,48,40,32,16,160,16,32,40,48,16,80,16,96,40,32,16,120,16,32,40,64,16,80,16,48,40,32,16,
49:  133,42,42,42,42,42,42,84,42,42,42,42,42,42,84,42,42,42,42,42,42,84,42,42,42,42,42,42,84,42,42,42,42,42,42,84,42,42,42,42,42,42,84,42,42,42,42,42,42,
50:  195,20,60,20,60,40,60,20,60,20,120,20,60,20,60,40,60,20,60,20,120,20,60,20,60,65,60,20,60,20,120,20,60,20,60,40,60,20,60,20,120,20,60,20,60,40,60,20,60,20,