OFFSET
1,1
COMMENTS
Take 2019; start with 2; jump over 2 cells to the right (as the even digits always move to the right); write 0 on the landing cell; jump over 0 cell to the right (which is the same as moving to the next cell to the right) and write 1 on the landing cell; as 1 is odd, jump over 1 cell to the left; write 9 on the landing cell; jump now over 9 cells to the left and mark A (for "Arrival") on the landing cell. The result will look like this (a dot is a cell): A.......2.901
As this A cell is not the same as the starting one (with "2"), 2019 is not a boomerang number. If we had taken 2011, we would have come back on the starting 2, like this:
2011
2..0
2..01
2.101
A.101
This is why 2011 is in the sequence and 2019 not.
Note that a cell, empty or not, is only a stopover: it can be used several times by different digits.
There are 263499 boomerang numbers < 10^7.
A boomerang number is easy to find, knowing the hereunder definition:
Integers B such that (the number of even digits + the sum of those) = (the number of odd digits + the sum of those).
Note: this sequence is not related to A256174 ("Boomerang fractions").
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..28444
EXAMPLE
7308403 is a boomerang number as we have 4 even digits with sum 12 (4+12=16) and 3 odd digits with sum 13 (3+13=16).
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, May 19 2019
STATUS
approved