A109167 a(n) = least nonnegative integer such that n appears a(n) times.

1, 2, 1, 0, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18

Offset: 0

Author

Rick L. Shepherd, Jun 20 2005

Keywords

• nonn
• changed

Comments

The concatenation of the first four terms' (decimal) digits gives 1210 = A046043(1).

Examples

			Note that we do not need to specify a(0) explicitly. Indeed, a(0) = 1 as it cannot be 0. a(1) = 2 as it cannot be 0 or 1.
		

Links

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

Crossrefs

Cf. A046043 (Autobiographical numbers), A001462 (Golomb's sequence).

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    alst = [1, 2, 1, 0, 4, 4, 4, 4]
    yield from alst
    for n in count(5):
        add = [n]*alst[n]
        yield from add
        alst.extend(add)
print(list(islice(agen(), 79))) # Michael S. Branicky, Aug 25 2025