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

[Robert Israel]

I meant 10*n, not concatenation. 


Sent from my Samsung Galaxy smartphone.


-------- Original message --------
From: David Seal <david.j.seal at gwynmop.com> 
Date:2019-08-27  2:03 PM  (GMT-05:00) 
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
Cc:  
Subject: [seqfan] Re: N = 3417. Now replace a digit by the "multiply" sign 

No, at least if I've understood the definition correctly:

101 is a hit because 1*1 = 1 divides it.

10101 is not a hit because neither 1*101 = 101 nor 101*1 = 101 divides it. (Nor does 10*01 = 10. The definition doesn't seem to allow that erasure, but it means that my answer of "No" is not affected if I've misunderstood that point.)

David


> On 27 August 2019 at 17:30 Robert Israel <israel at math.ubc.ca> wrote:
> 
> 
> 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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> 
> 
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