cp's OEIS Frontend

This sequence is strictly increasing since if a(n) is attained by the sum of digits of k, then the final digit of k is 3 and (k - (k mod 3))*4/3 + 3 is the same digits with a new second-least significant 1, 2 or 3 inserted, and so a(n+1) >= a(n) + 1.

Terms can be derived from A357425 by a(n) = s for the largest s where A357425(s) has n digits in base 4/3.

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).

Only a finite number of numbers have sum of digits n (the largest is A364779(n)).