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

hv at crypt.org hv at crypt.org
Wed Aug 28 14:56:55 CEST 2019

```I think it is worth making clear in the definition whether fragments are
allowed to have leading zeroes: 1001 is in the sequence iff you are allowed
to split it as 1*01.

Hugo

Neil Sloane <njasloane at gmail.com> wrote:
:Eric, That sequence is worth including in the OEIS - can you submit it?
:(If you already did, could you post the A-number here?)
:Best regards
:Neil
:
:Neil J. A. Sloane, President, OEIS Foundation.
:11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
:Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
:Email: njasloane at gmail.com
:
:
:
:On Tue, Aug 27, 2019 at 4:12 PM Robert Israel <israel at math.ubc.ca> wrote:
:
:> 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: Ã‰ric 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 Â« hits Â»
:> > (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,
:> > Ã‰.

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