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

1,3

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

Links

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A082746 A098313 A098311 * A230086 A333404 A227082

Adjacent sequences: A342262 A342263 A342264 * A342266 A342267 A342268

Keyword

base,nonn,fini,full

Author

Eric Angelini and Carole Dubois, Mar 07 2021

Status

approved