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

%I A342264 #19 Jul 16 2025 16:49:49
%S A342264 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,
%T A342264 27,28,38,39,49,66,45,34,35,44,55,56,57,58,59,67,46,68,47,69,48,77,36,
%U A342264 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
%N A342264 Lexicographically earliest sequence of distinct nonnegative terms such that both a(n) and a(n) + a(n+1) have digits in nondecreasing order.
%C A342264 10 is obviously the first integer not present in the sequence as 1 > 0.
%H A342264 Robert Israel, <a href="/A342264/b342264.txt">Table of n, a(n) for n = 1..4000</a>
%e A342264 a(10) = 9 and a(11) = 13 sum up to 22: the three numbers have digits in nondecreasing order;
%e A342264 a(11) = 13 and a(12) = 11 sum up to 24 (same property);
%e A342264 a(12) = 11 and a(13) = 12 sum up to 23 (same property);
%e A342264 etc.
%p A342264 ND[1]:= [$1..9]:
%p A342264 for d from 2 to 5 do
%p A342264    ND[d]:= map(proc(t) local j; seq(10*t + j,j=(t mod 10) .. 9) end proc, ND[d-1])
%p A342264 od:
%p A342264 S:= [seq(op(ND[i]),i=1..5)]): nS:= nops(S):
%p A342264 isnd:= proc(x) member(x,ND[ilog10(x)+1]) end proc:
%p A342264 R:= 0: t:= 0:
%p A342264 for count from 2 to 100 do
%p A342264   found:= false;
%p A342264   for i from 1 to nS do
%p A342264     if isnd(t + S[i]) then
%p A342264       R:= R, S[i];
%p A342264       t:= S[i];
%p A342264       S:= subsop(i=NULL, S);
%p A342264       nS:= nS-1;
%p A342264       found:= true;
%p A342264       break
%p A342264     fi;
%p A342264   od;
%p A342264   if not found then break fi;
%p A342264 od:
%p A342264 R; # _Robert Israel_, Jul 14 2025
%o A342264 (Python)
%o A342264 def nondec(n): s = str(n); return s == "".join(sorted(s))
%o A342264 def aupton(terms):
%o A342264   alst = [0]
%o A342264   for n in range(2, terms+1):
%o A342264     an = 1
%o A342264     while True:
%o A342264       while an in alst: an += 1
%o A342264       if nondec(an) and nondec(alst[-1]+an): alst.append(an); break
%o A342264       else: an += 1
%o A342264   return alst
%o A342264 print(aupton(74)) # _Michael S. Branicky_, Mar 07 2021
%Y A342264 Cf. A009994 (numbers with digits in nondecreasing order), A342265 and A342266 (variations on the same idea).
%K A342264 nonn,look,base
%O A342264 1,3
%A A342264 _Eric Angelini_ and _Carole Dubois_, Mar 07 2021