A378949 Numbers with monotonically increasing digits, increasing by only 0 or 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 22, 23, 33, 34, 44, 45, 55, 56, 66, 67, 77, 78, 88, 89, 99, 111, 112, 122, 123, 222, 223, 233, 234, 333, 334, 344, 345, 444, 445, 455, 456, 555, 556, 566, 567, 666, 667, 677, 678, 777, 778, 788, 789, 888, 889, 899, 999

Offset: 1

Author

Randy L. Ekl, Dec 18 2024

Keywords

• nonn
• base

Examples

			33 is a term since the digits are monotonically increasing and their difference is 0.
34 is also a term since the digits are monotonically increasing and their difference is 1.
35 is not a term since the difference in consecutive digits is not 0 or 1.
32 is not a term since the digits are decreasing.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A378808, A378774.

Programs

Maple

extend:= proc(k) local m,d;
  m:= 10^ilog10(k);
  d:= floor(k/m);
  if d = 1 then 10*m+k else (d-1)*10*m+k, d*10*m+k fi
end proc:
R:= $1..9:
A:= [R]:
for i from 2 to 5 do
  A:= map(extend,A);
  R:= R, op(sort(A));
od:
R; # Robert Israel, Jan 18 2025

Mathematica

Select[Range[1000],SubsetQ[{0, 1}, Union@ Differences@ IntegerDigits[#]] &] (* James C. McMahon, Dec 21 2024 *)

Python

from itertools import count, islice
def bgen(last, d):
    if d == 0: yield tuple(); return
    t = (1, 9) if last == None else (last, min(last+1, 9))
    for i in range(t[0], t[1]+1): yield from ((i, )+r for r in bgen(i, d-1))
def agen(): # generator of terms
    yield from (int("".join(map(str, i))) for d in count(1) for i in bgen(None, d))
print(list(islice(agen(), 62))) # Michael S. Branicky, Dec 18 2024

Extensions

Offset corrected by James C. McMahon, Dec 21 2024