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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 10 is obviously the first integer not present in the sequence as 1 > 0. LINKS 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 AUTHOR Eric Angelini and Carole Dubois, Mar 07 2021 STATUS approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)