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

Author

Eric Angelini and Carole Dubois, Mar 07 2021

Keywords

• nonn
• look
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

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