OFFSET
0,3
COMMENTS
A largest integer exists since only a finite number of trailing 0 digits are possible, since each is a factor 4/3.
Each term k >= 3 has final digit d = k mod 4 which is always d < r where r = k mod 3 (and hence d = 0 or 1), since otherwise (k - r)*4/3 + r would split d into two final digits {d-r, r} for a larger number with the same sum of digits.
This sequence is strictly increasing since final digit d = 0 or 1 (and also a(2) = 2) can be incremented so that a(n)+1 is a candidate value for a(n+1).
LINKS
Kevin Ryde, Table of n, a(n) for n = 0..150
Kevin Ryde, C Code
PROG
(C) See links.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Kevin Ryde, Aug 13 2023
STATUS
approved