A084383 a(0)=0; for n>0, a(n) = smallest number that is not a concatenation of any number of distinct earlier terms in increasing order.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 118, 119, 200, 201, 202

Offset: 0

Author

Amarnath Murthy, May 29 2003

Keywords

• nonn
• base
• changed

Comments

After 11 we can see 1,2 -> 12, 1,3 -> 13, etc., but not 20.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000

Crossrefs

Hannah Rollman's numbers: A048991, A048992.

Programs

Python

from itertools import islice
def incats(s, L):
    if s == "": return True
    return any(s.startswith(w) and incats(s[len(w):], L[i+1:]) for i, w in enumerate(L))
def agen(): # generator of terms
    L, an, s = ["0"], 1, "1"
    yield from [0]
    while True:
        yield an
        L.append(s)
        while incats((s:=str(an)), L):
            an += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Feb 01 2024

Extensions

More terms from Patrick De Geest, Jun 03 2003