[seqfan] New "knife" sequence

[Eric Angelini]

Hello SeqFans,

The « knife » sequence https://oeis.org/A243357
could have a « sister » one (where the digit dividing Z
is not the last one of Z but the digit immediately
to the right of the "cut".

Definition:

> Lexicographically earliest sequence with property
that if a vertical line is drawn between any pair of
adjacent digits, the number Z formed by the digits
to the left of the line is divisible by the first
digit following Z.

The pattern of this new sequence is strange! (if I
did not make too many mistakes):

S = 1,11,3,7,71,31,111,113,33,117,331,1111,1311,1331,9,...

Best,
É.