A378808 Numbers with monotonically decreasing digits, decreasing by only 0 or 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 32, 33, 43, 44, 54, 55, 65, 66, 76, 77, 87, 88, 98, 99, 100, 110, 111, 210, 211, 221, 222, 321, 322, 332, 333, 432, 433, 443, 444, 543, 544, 554, 555, 654, 655, 665, 666, 765, 766, 776, 777, 876, 877, 887, 888, 987, 988, 998, 999

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Example

32 is a term since it has monotonically decreasing digits whose difference is at most 1.
33 is a term since it also has monotonically decreasing digits whose difference is at most 1.

Mathematica

Select[Range[999], SubsetQ[{0, 1}, -Differences[IntegerDigits[#]]] &] (* Stefano Spezia, Dec 08 2024 *)

Prog

(Python)
from itertools import count, islice
def bgen(last, d):
    if d == 0: yield tuple(); return
    t = (1, 9) if last == None else (max(0, last-1), last)
    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 08 2024

Crossrefs

Cf. A009996, A064222, A378775.

Sequence in context: A337925 A130575 A330760 * A064222 A261294 A390052

Adjacent sequences: A378805 A378806 A378807 * A378809 A378810 A378811

Keyword

nonn,base

Author

Randy L. Ekl, Dec 07 2024

Status

approved