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

0,2

Links

Table of n, a(n) for n=0..66.

Gavin Lupo, Image of the first 10000 terms

Example

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).

Prog

(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

Crossrefs

Cf. A000002, A107353, A339853.

Sequence in context: A040109 A317054 A292690 * A362551 A036188 A013617

Adjacent sequences: A362368 A362369 A362370 * A362372 A362373 A362374

Keyword

nonn,base

Author

Gavin Lupo, Apr 17 2023

Status

approved