A375306 Terms as well as digits fit the even/odd/odd pattern; this is the lexicographically earliest injective sequence with this property.

0, 1, 3, 2, 5, 7, 4, 9, 101, 10, 11, 21, 12, 13, 23, 14, 15, 25, 16, 17, 27, 18, 19, 29, 30, 31, 41, 32, 33, 43, 34, 35, 45, 36, 37, 47, 38, 39, 49, 50, 51, 61, 52, 53, 63, 54, 55, 65, 56, 57, 67, 58, 59, 69, 70, 71, 81, 72, 73, 83, 74, 75, 85, 76, 77, 87, 78, 79, 89, 90, 91, 211, 6, 93, 213, 8, 95, 215, 2110, 97

Offset: 1

Author

Eric Angelini, Aug 11 2024

Keywords

• base
• nonn

Examples

			a(7) = 4, a(8) = 9, a(9) = 101, a(10) = 10; terms follow the even/odd/odd pattern and so do their digits: 4/9/1 and 0/1/1.
		

Links

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

Crossrefs

Cf. A217555, A375305.

Programs

Python

from itertools import count, islice, repeat
def c(s, i):
    return all(int(d)%2 == int((i+j)%3 > 0) for j, d in enumerate(s))
def agen(): # generator of terms
    seen, s = set(), 0
    for n in count(0):
        eo = int(n%3 > 0)
        an = next(k for k in count(eo, 2) if k not in seen and c(str(k), s))
        yield an
        seen.add(an)
        s += len(str(an))
print(list(islice(agen(), 99))) # Michael S. Branicky, Aug 11 2024