A363408 Squares whose base-3 expansion has no 2.

0, 1, 4, 9, 36, 81, 121, 256, 324, 361, 729, 841, 1089, 2304, 2916, 3025, 3249, 6561, 6889, 7569, 9801, 20449, 20736, 26244, 26569, 27225, 29241, 59049, 60025, 62001, 68121, 68644, 88209, 177241, 184041, 186624, 203401, 236196, 237169, 239121, 245025, 263169, 531441, 534361, 540225, 558009

Offset

1,3

Comments

Squares that are the sum of distinct powers of 3.

If k is a term, then so is 9*k.

The only square whose base-3 expansion has no 1 is 0.

Links

Robert Israel, Table of n, a(n) for n = 1..665

Formula

a(n) = A176189(n-1)^2 for n>=2. - Alois P. Heinz, Jun 07 2023

Example

a(5) = 36 is a term because 36 = 6^2 = 3^2 + 3^3.

Maple

R:= {0, 1};
S:= {1};
for i from 1 to 20 do
  S:= map(t -> (3*t, 3*t+1), S);
  R:= R union select(issqr, S)
od:
R;

Mathematica

Select[Range[0, 1000]^2, ! MemberQ[IntegerDigits[#, 3], 2] &] (* Amiram Eldar, Jun 01 2023 *)

Prog

(Python)
from gmpy2 import digits
def okA176189(n): return "2" not in digits(n*n, 3)
print([k**2 for k in range(1000) if okA176189(k)]) # Michael S. Branicky, Jun 07 2023

Crossrefs

Intersection of A000290 and A005836. Cf. A363428.

Cf. A176189.

Sequence in context: A326182 A053057 A118547 * A115700 A029806 A133125

Adjacent sequences: A363405 A363406 A363407 * A363409 A363410 A363411

Keyword

nonn,base

Author

Robert Israel, May 31 2023

Status

approved