Long Number With Special Property

[kuiperbelt]

If we start with 2 and build up one digit at a time creating the smallest number with a certain property we get the number 20120456708436008 before we have to stop. What do we get if we start with the number one?

[ClareTG0ld]

I looked this up, because I was curious if this were a well-known problem. It possibly isn't, but in any case I now know the solution and won't contribute an answer in case anybody else wants a go. But I will give a hint, or possibly just a clarification: the "build up one digit at a time" part means that we're generating a sequence 2, 20, 201, 2012 etc., and just adding a digit at the end until we "have to stop".

[Etch]

Spoiler Alert - my candidate for "Best Answer" below
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10200056405. Each number on the way is the smallest number to start with the previous number and be divisible by its own length.

[Radagast]

I looked this up as well. I would never have got it. Here's a Fortran program starting with 1 to 9:

program nums
integer(16)::j,n,k
do i=1,9
j=i
n=2
write(*,"(1i1)",advance="no") j
k=0
do while(k .ne. 10)
if(mod(j*10+k,n)==0) then
write(*,"(1i1)",advance="no") k
j=j*10+k
k=0
n=n+1
else
k=k+1
end if
end do
print *
end do
end program nums

it can be run here:
https://www.tutorialspoint.com/compile_fortran_online.php

[1581960]

I would have been totally stumped without
https://oeis.org/search?q=A098143&go=Search

[Etch]

The question appears here ("Mindset by 700", bottom of page 4), as does the answer I provided (page 9):
https://extras.thetimes.co.uk/web/pdfs/fb5f9c02c1639d63639a4ccdd6875776.pdf

[kuiperbelt]

Thank you to all contributors on this thread. Your honesty is admirably refreshing and without exception each and everyone of you are a credit to the AB forum!! I am not going to award BA as you have all behaved with such probity and I am unable to single out any one particular individual. Once again many thanx to you all!!

[ichkeria]

Rather more honest than you were in not acknowledging the source

[douglas9401]

Are these questions just for the amusement of the mathematically gifted?
I seem to remember it all started as 'homework help' but seems to have moved on.

I only ask because I'm not great with big sums. :-)

[bobbinwales]

I'm confused... nothing new there.
. but just dont see the point of this. The infinity stuff is interesting as is your maths problems usually....but this seems so contrived.but I'm in a minority as others seemed to like the challenge.