[seqfan] Smallest hitters

[Eric Angelini]

Hello Sedfans,
if we call "wilsonization" the operation visible
here http://oeis.org/A100787 we could indeed
wilsonize any integer to produce a (not strictly)
increasing sequence.
Take 137, for instance and start a sequence S
where the differences "d" between two consecutive
terms of S spell, digit by digit, the sequence S
itself:

S = 137 138 141 148 149 152 160 161 165 166 ...
d =    1   3   7   1   3   8   1   4   1

We see that 137 "hits" 166 (for instance) -- but
is 137 the smallest integer hitting 166? No, it
is 1 (as one will see following the above link).

What is the sequence of the "smallest hitters"
(SH) of the natural numbers?

I guess it starts:

n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
SH = 1 1 3 1 5 3 7 1 9  5  5  3  3  5  3  1  1 ...

Best,
É.