A342265 Lexicographically earliest sequence of distinct nonnegative terms such that both a(n) and the cumulative sum a(1)+a(2)+...+a(n) have digits in nondecreasing order.

0, 1, 2, 3, 5, 4, 7, 6, 8, 9, 11, 12, 44, 13, 14, 16, 22, 45, 15, 18, 23, 55, 24, 88, 33, 77, 34, 78, 111, 333, 17, 19, 79, 29, 89, 25, 99, 199, 112, 444, 26, 28, 56, 35, 188, 113, 119, 556, 114, 999, 122, 1199, 888, 123, 4444, 36, 66, 124, 118, 222, 445, 115, 129, 67, 133, 667, 134, 68, 889, 223

Offset: 1

Author

Eric Angelini and Carole Dubois, Mar 07 2021

Keywords

• base
• nonn
• fini
• full

Comments

10 is obviously the first integer not present in the sequence as 1 > 0.

The last term is a(173) = 122222, at which point the cumulative sum is 12467999, and the sequence cannot be extended. - Michael S. Branicky, Feb 05 2024

Examples

			Terms a(1) = 0 to a(5) = 5 sum up to 11: those six numbers have digits in nondecreasing order;
terms a(1) = 0 to a(6) = 4 sum up to 15: those seven numbers have digits in nondecreasing order;
terms a(1) = 0 to a(7) = 7 sum up to 22: those eight numbers have digits in nondecreasing order; etc.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..173

Crossrefs

Cf. A009994 (numbers with digits in nondecreasing order), A342264 and A342266 (variations on the same idea).

Programs

Python

def nondec(n): s = str(n); return s == "".join(sorted(s))
def aupton(terms):
  alst = [0]
  for n in range(2, terms+1):
    an, cumsum = 1, sum(alst)
    while True:
      while an in alst: an += 1
      if nondec(an) and nondec(cumsum + an): alst.append(an); break
      else: an += 1
  return alst
print(aupton(100)) # Michael S. Branicky, Mar 07 2021