A038103 Numbers k such that k is a substring of its base-3 representation.

0, 1, 2, 10, 20, 21, 102, 110, 210, 211, 212, 220, 1011, 1112, 1121, 2022, 12101, 12102, 12112, 12122, 10121021, 10121022, 12222212, 102121110, 102121120, 200121022, 1001120220, 2011001102, 2012012221, 2100221021, 2102111111

Offset: 1

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base

Examples

			12101 = base 10 -> 121{12101}2 = base 3.
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..210 (terms 1..151 from Giovanni Resta).
• Hans Havermann, pdf file showing the corresponding A350573 terms and illustrating the ternary embeddings (for terms 1..210).

Crossrefs

Cf. A038102-A038106, A228050-A228052, A227549, A350573.

Programs

Python

from sympy.ntheory.digits import digits
from itertools import count, islice, product
def agen(): # generator of terms
    yield 0
    for d in count(1):
        for first in "12":
            for rest in product("012", repeat=d-1):
                s = first + "".join(rest)
                if s in "".join(str(d) for d in digits(int(s), 3)[1:]):
                    yield int(s)
print(list(islice(agen(), 31))) # Michael S. Branicky, Jan 08 2022

Python

from itertools import count, islice
from gmpy2 import digits
def A038103_gen(): return (int(s) for s in (digits(n,3) for n in count(0)) if s in digits(int(s),3))
A038103_list = list(islice(A038103_gen(),30)) # Chai Wah Wu, Jan 09 2022