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

Offset

0,3

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

Prog

(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

Crossrefs

Hannah Rollman's numbers: A048991, A048992.

Sequence in context: A247758 A247757 A247754 * A032873 A072543 A009996

Adjacent sequences: A084380 A084381 A084382 * A084384 A084385 A084386

Keyword

nonn,base

Author

Amarnath Murthy, May 29 2003

Extensions

More terms from Patrick De Geest, Jun 03 2003

Status

approved