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

1,3

Comments

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

Links

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

Example

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.

Maple

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

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 = 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

Crossrefs

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

Sequence in context: A081549 A085889 A342951 * A094823 A032973 A174887

Adjacent sequences: A342261 A342262 A342263 * A342265 A342266 A342267

Keyword

nonn,look,base

Author

Eric Angelini and Carole Dubois, Mar 07 2021

Status

approved