A191598 a(1)=1. Then, if the first n terms contain all the numbers 1 to n, a(n+1)=2*a(n), otherwise a(n+1) is the smallest number not already in the sequence.

1, 2, 4, 3, 6, 5, 10, 7, 8, 9, 18, 11, 12, 13, 14, 15, 16, 17, 34, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 66, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 130

Offset: 1

Author

Greg Knowles, Jun 08 2011

Keywords

• nonn
• easy

Examples

			There are no gaps with just one term, so we double to get a(2)=2. Still no gaps, so we double again to get a(3)=4. Now 3 has not appeared yet, so a(4)=3. The sequence is compact again, so we double to get a(5)=6.
		

Links

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

Programs

Python

from itertools import count, islice
def agen():  # generator of terms
    an, aset, m = 1, {1}, 2
    for n in count(1):
        yield an
        an = 2*an if m > n else m
        aset.add(an)
        while m in aset: m += 1
print(list(islice(agen(), 67))) # Michael S. Branicky, Nov 13 2024