[seqfan] Sequence of digit sum divisibility

[Jack Brennen]

Today, I saw a problem posed as such:

    "Prove that there are infinitely many numbers not containing the digit 0, that are divisible by the sum of their digits."

    Source:  http://www.scribd.com/doc/50712437/Number-Theory
    Problem 5.2.3

The proposed solution was to prove by induction that (10^(3^n)-1)/9 is such a number for any n>=0.


However, I started thinking about constellations of such numbers.  Obviously, you can only have nine consecutive such numbers,
the first such 9-tuple being the "trivial" (1,2,3,4,5,6,7,8,9).

The next such 9-tuples seem to be those starting with:

142813628717821
253323932621811
1234954171531131
1713763544613181
3713154346661821
5953112416611411
8711631351783421
11853531183574141
12191214257422251
17137635446131261
19941476493818971
21342541323383331
25628491758925521
28665872459864731
32674635925331471
33637395433589721
38442737638388241
43566181233775271
45122116277838671
47715341351277671
56411383343515261
59265887192515161
64311981821287271
69171996587934331
69795167728366171
75283694541843561
75722172144418871
79871332261921271
81118141111687741
84539137394111471
89699721156239121
92318812614428471
94542622211157181
96591526766935291
96694399875626381

The first of those doesn't show up in a Google search, leading me to believe that this sequence
has never been investigated.

First, is this of interest for OEIS?  Second, if so, can somebody verify that those are correct?

   Jack