A101807 - OEIS

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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

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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)))