A342266 -id:A342266 - cp's OEIS frontend

A342264 Lexicographically earliest sequence of distinct nonnegative terms such that both a(n) and a(n) + a(n+1) have digits in nondecreasing order.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 11, 12, 14, 15, 18, 16, 17, 19, 25, 22, 23, 24, 33, 26, 29, 27, 28, 38, 39, 49, 66, 45, 34, 35, 44, 55, 56, 57, 58, 59, 67, 46, 68, 47, 69, 48, 77, 36, 78, 37, 79, 88, 89, 99, 123, 111, 112, 113, 114, 115, 118, 116, 117, 119, 125, 122, 124, 133, 126, 129, 127, 128, 138

Offset: 1

Eric Angelini and Carole Dubois, Mar 07 2021

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

			a(10) = 9 and a(11) = 13 sum up to 22: the three numbers have digits in nondecreasing order;
a(11) = 13 and a(12) = 11 sum up to 24 (same property);
a(12) = 11 and a(13) = 12 sum up to 23 (same property);
etc.

Robert Israel, Table of n, a(n) for n = 1..4000

Cf. A009994 (numbers with digits in nondecreasing order), A342265 and A342266 (variations on the same idea).

ND[1]:= [$1..9]:
for d from 2 to 5 do
   ND[d]:= map(proc(t) local j; seq(10*t + j,j=(t mod 10) .. 9) end proc, ND[d-1])
od:
S:= [seq(op(ND[i]),i=1..5)]): nS:= nops(S):
isnd:= proc(x) member(x,ND[ilog10(x)+1]) end proc:
R:= 0: t:= 0:
for count from 2 to 100 do
  found:= false;
  for i from 1 to nS do
    if isnd(t + S[i]) then
      R:= R, S[i];
      t:= S[i];
      S:= subsop(i=NULL, S);
      nS:= nS-1;
      found:= true;
      break
    fi;
  od;
  if not found then break fi;
od:
R; # Robert Israel, Jul 14 2025

def nondec(n): s = str(n); return s == "".join(sorted(s))
def aupton(terms):
  alst = [0]
  for n in range(2, terms+1):
    an = 1
    while True:
      while an in alst: an += 1
      if nondec(an) and nondec(alst[-1]+an): alst.append(an); break
      else: an += 1
  return alst
print(aupton(74)) # Michael S. Branicky, Mar 07 2021

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.

Original entry on oeis.org

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

Eric Angelini and Carole Dubois, Mar 07 2021

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

			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.

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

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

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

cp's OEIS Frontend

A342264 Lexicographically earliest sequence of distinct nonnegative terms such that both a(n) and a(n) + a(n+1) have digits in nondecreasing order.

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