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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.

%I A342265 #14 Feb 05 2024 18:07:37
%S A342265 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,
%T A342265 34,78,111,333,17,19,79,29,89,25,99,199,112,444,26,28,56,35,188,113,
%U A342265 119,556,114,999,122,1199,888,123,4444,36,66,124,118,222,445,115,129,67,133,667,134,68,889,223
%N 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.
%C A342265 10 is obviously the first integer not present in the sequence as 1 > 0.
%C A342265 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
%H A342265 Michael S. Branicky, <a href="/A342265/b342265.txt">Table of n, a(n) for n = 1..173</a>
%e A342265 Terms a(1) = 0 to a(5) = 5 sum up to 11: those six numbers have digits in nondecreasing order;
%e A342265 terms a(1) = 0 to a(6) = 4 sum up to 15: those seven numbers have digits in nondecreasing order;
%e A342265 terms a(1) = 0 to a(7) = 7 sum up to 22: those eight numbers have digits in nondecreasing order; etc.
%o A342265 (Python)
%o A342265 def nondec(n): s = str(n); return s == "".join(sorted(s))
%o A342265 def aupton(terms):
%o A342265   alst = [0]
%o A342265   for n in range(2, terms+1):
%o A342265     an, cumsum = 1, sum(alst)
%o A342265     while True:
%o A342265       while an in alst: an += 1
%o A342265       if nondec(an) and nondec(cumsum + an): alst.append(an); break
%o A342265       else: an += 1
%o A342265   return alst
%o A342265 print(aupton(100)) # _Michael S. Branicky_, Mar 07 2021
%Y A342265 Cf. A009994 (numbers with digits in nondecreasing order), A342264 and A342266 (variations on the same idea).
%K A342265 base,nonn,fini,full
%O A342265 1,3
%A A342265 _Eric Angelini_ and _Carole Dubois_, Mar 07 2021