[seqfan] A message from Eric Angelini

[Neil Sloane]

He says he can't send anything to the list directly so he asked me to post
this on his behalf. It looks like a very nice idea.


Hello SeqFans,

I've had the idea of stuffable numbers a few weeks ago; take 2018 for
instance and open it:

2018 becomes 2..01.8 (two spaces after 2, no space after the 0, one space
after 1, nothing after 8 — and, in general, k spaces after each  digit k,
except the last one) .

One pushes then an integer in the empty spaces, for instance 136:

2..01.8 becomes 2130168.

Let's call 136 the stuff, and 2130168 the stuffed. If the stuffed is
divisible by the stuff, we will call the starting integer a stuffable
number (this
is the case here for 2018, as 2130168 divided by 136 gives 15663).

Remark 1: no stuff can begin with a leading zero.

Remark 2: some stuffable numbers admit more then one stuff – like 20,
hereunder:


20 becomes 2..0 and the following stuffed are divisible by their respective
stuffs :

2100 divided by 10 is 210

2160 divided by 16 is 135

2200 dividid by 20 is 110

2250 divided by 25 is 90

2400 divided by 40 is 60

2500 divided by 50 is 50.


Question: what would a sequence of stuffables look like? It would start
with 10, then 11, then 12, 13, 14, 15, 16, 17, 18, 19 (as all those can be
stuffed by 1 at least), then 20, 21 (stuff = 23), 22 (stuff = 11), but not
23 (impossible to stuff, I guess).

[That is because 2003 is prime. So 2003+10*i is not divisible by i for any
i in the range 10 to 99. - Neil]

A few more sequences based on this idea are possible -- and might enter the
OEIS, if of interest, of course.


[Some more data here, in a French

communication, under Tom Wesselmann's Bras:

https://cinquantesignes.blogspot.com/2018/11/wesselmann-stuffable-numbers-taupes-et.html
]

Best,

É.