A101807 Start with 0 and decide that each digit d of the sequence means that the next integer cannot be of length d. To build the sequence take the smallest available integer not yet in the sequence.

0, 1, 10, 11, 2, 12, 13, 3, 14, 4, 15, 5, 6, 16, 7, 8, 17, 9, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 100, 31, 101, 32, 102, 103, 104, 33, 105, 34, 106, 35, 107, 36, 108, 37, 109, 38, 110, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 111, 51, 52

Offset

1,3

Comments

The first 0 means: "next integer cannot be of length zero", thus "1" ("1" being the first available integer not yet in the sequence). Now this "1" reads: "next integer cannot be of length one", thus 10 ("10" being the first two-digit integer not yet in the sequence). The next digit to be read is the "1" digit of this "10": "next integer cannot be of length one", thus 11 ("11" being the smallest two-digit integer not yet in the sequence). The next digit to be read is the "0" digit of "10" which produces "2" ("2" is not of length zero and is the smallest available integer after "1", already in the sequence) "next 10 11 2 12 13 3 14 4 15

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an, aset, dlst, m = 0, {0}, [None, 0], 1
    for n in count(1):
        yield an
        an = next(k for k in count(m) if k not in aset and len(str(k)) != dlst[n])
        aset.add(an)
        dlst.extend(map(int, str(an)))
        while m in aset: m += 1
print(list(islice(agen(), 65))) # Michael S. Branicky, Oct 04 2024

Crossrefs

Sequence in context: A176998 A328752 A173821 * A248025 A303501 A368347

Adjacent sequences: A101804 A101805 A101806 * A101808 A101809 A101810

Keyword

base,easy,nonn

Author

Eric Angelini, Jan 27 2005

Extensions

Offset changed and a(33) and beyond from Michael S. Branicky, Oct 04 2024

Status

approved