# [seqfan] Re: N = 3417. Now replace a digit by the "multiply" sign

Robert Israel israel at math.ubc.ca
Tue Aug 27 18:30:17 CEST 2019

```Is it not true that 10 n is a hit whenever n is?

Sent from my Samsung Galaxy smartphone.

-------- Original message --------
From: Éric Angelini <bk263401 at skynet.be>
Date:2019-08-27  10:57 AM  (GMT-05:00)
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc:
Subject: [seqfan] N = 3417. Now replace a digit by the "multiply" sign

Hello SeqFans,

Take an integer N (for example N = 3417).
Erase one of N's digits to form integers P and Q.
(For N = 3417, erasing 4 produces P = 3 and Q = 17).
If P*Q divides N, we have a hit.
(this is the case here as 3*17 = 51 and 3417/51 = 67
although the other possible erasure doesn't produce
an integer: 34*7 = 238 and 3417/238 = 14.35714...)

Jean-Marc Falcoz has computed 10,000 such « hits »
(with N > 99 and Q that cannot have a leading 0,
except if Q = 0); he noticed that the density of
hits decreases dramatically when N gets bigger and
bigger. Which leads to this: is the hit-sequence
finite? More pictures and data here, for those
who might be interested:
https://bit.ly/2Lag2Fh (in French).
Best,
É.

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