A018827 Numbers n such that n is a substring of its square in base 3 (written in base 10).

0, 1, 3, 7, 9, 27, 32, 43, 81, 131, 243, 287, 706, 729, 1330, 1390, 1679, 1832, 2187, 2899, 3848, 4170, 5234, 6436, 6561, 11544, 12510, 14261, 19308, 19683, 30433, 33181, 34135, 35203, 35323, 37530, 38669, 42783, 59049, 72070, 79583, 93539, 99543

Offset

1,3

Links

Table of n, a(n) for n=1..43.

Mathematica

Select[Range[0, 10^5], StringContainsQ[IntegerString[#^2, 3], IntegerString[#, 3]] &] (* Paolo Xausa, Apr 05 2024 *)

Prog

(Python)
from sympy.ntheory import digits
def s(n, base=3): return "".join(map(str, digits(n, base)[1:]))
def ok(n): return s(n) in s(n**2)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Apr 04 2024

Crossrefs

Cf. A018826 (base 2), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Sequence in context: A098338 A033958 A352016 * A249664 A057840 A339614

Adjacent sequences: A018824 A018825 A018826 * A018828 A018829 A018830

Keyword

nonn,base

Author

David W. Wilson

Status

approved