A363490 Lexicographically earliest infinite sequence of distinct terms > 0 such that one digit of a(n) is strictly smaller than one digit of a(n+1).

1, 2, 3, 4, 5, 6, 7, 8, 19, 12, 13, 14, 15, 16, 17, 18, 20, 10, 11, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Digit 1 is < 2; 2 is < 3; etc. Then comes 8: if we write 9 after 8, the sequence stops (as there is no digit > 9). This forces a(9) = 19 (instead of 9) as the smallest available integer not leading to a contradiction. Integers consisting only of 9s (9, 99, 999, etc.) will thus never be part of the sequence.

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, aset, mink = 1, {1}, 2
    while True:
        yield an
        k, m = mink, min(str(an))
        while k in aset or (s:=set(str(k))) == {"9"} or max(s) <= m:
            k += 1
        an = k
        aset.add(an)
        while mink in aset or set(str(mink)) == {"9"}:
            aset.discard(mink); mink += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Jun 05 2023

Crossrefs

Cf. A294069.

Sequence in context: A055557 A173577 A103205 * A039127 A024650 A037343

Adjacent sequences: A363487 A363488 A363489 * A363491 A363492 A363493

Keyword

base,nonn

Author

Eric Angelini, Jun 05 2023

Status

approved