A362371 a(0)=0. For each digit in the sequence, append the smallest unused integer that contains that digit.

0, 10, 1, 20, 11, 2, 30, 12, 13, 21, 3, 40, 14, 22, 15, 23, 24, 16, 31, 4, 50, 17, 34, 25, 26, 18, 5, 27, 32, 28, 41, 19, 6, 33, 51, 42, 35, 60, 61, 7, 36, 43, 29, 45, 52, 46, 71, 8, 53, 62, 37, 38, 72, 82, 48, 44, 81, 91, 9, 56, 39, 63, 54, 100, 47, 92, 73

Offset: 0

Author

Gavin Lupo, Apr 17 2023

Keywords

• nonn
• base

Examples

			a(0) =  0
a(1) = 10 (from digit 0 in a(0)=0, smallest integer other than 0).
a(2) =  1 (from digit 1 in a(1)=10, smallest integer other than 10).
a(3) = 20 (from digit 0 in a(1)=10, smallest integer other than 0 and 10).
a(4) = 11 (from digit 1 in a(2)=1, smallest integer other than 1 and 10).
a(5) =  2 (from digit 2 in a(3)=20, smallest integer other than 20).
a(6) = 30 (from digit 0 in a(3)=20, smallest integer other than 0, 10, and 20).
		

Links

• Gavin Lupo, Image of the first 10000 terms

Crossrefs

Cf. A000002, A107353, A339853.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    s, aset, mink = "0", set(), 0
    for n in count(0):
        an = mink
        while an in aset or set(san:=str(an)) & {s[0]} == set(): an += 1
        s = s[1:] + san
        aset.add(an)
        yield an
        while mink in aset: aset.discard(mink); mink += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Apr 25 2023