Define the flipflop function, applied to a positive integer, as the result of having the 10^2i and 10^(2i+1) digits switch places.
Moreover, if the integer has an odd number of digits, append a leading zero to the left side of the number so that it can flipflop with the first nonzero digit.

For example, flipflop(9876) = 8967 and flipflop(1234567) is 10325476.

warm-up:
What is the smallest positive integer such that flipflop(m) = m*4?

octuple the number:
What is the smallest positive integer such that flipflop(n) = n*8?
In the case of multiplication by 8, I have found only one solution: are there any others?

(In reply to re: computer solution by Brian Smith)

With appropriate change to the addition routine, there was comfortable time to find some more solutions. The found sets are now:

Posted by Charlie on 2022-03-30 20:53:05