[seqfan] Playing with A036301

[Eric Angelini]

Hello Seqfans,
let's say that a(n+1) is obtained from a(n) like this:
- make the sum E of even digits of a(n)
- make the sum D of odd digits of a(n)
- let a(n+1) = a(n) - E + D

Example:
if a(n) = 2012 then a(n+1) = 2012 - 4 + 1 = 2009

Iterating from there would give 2009-2016-2009 (loop).

I've started to check the fate of the first 100 integers
and found a few other loops and fixed points -- if we call
"fixed points" the members of https://oeis.org/A036301
(Numbers n such that sum of even digits of n equals sum
of odd digits of n).

 0 is the first integer ending on A036301(1)
 5 is the first integer entering [11-13-17-25-28-18-11]
37 is the first integer entering [54-55-65-64-54]
93 is the first integer ending on A036301(2)
19 is the first integer ending on A036301(3)

Is the sequence 0,5,37,93,19,... worth entering the OEIS
(if correct)?
What about computing a(n+1) = a(n) + E - D instead?
Best,
É.