A176189 -id:A176189 - cp's OEIS frontend

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

Robert Israel, May 31 2023

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.

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

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

Intersection of A000290 and A005836. Cf. A363428.

Cf. A176189.

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;

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

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

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

A219115 Numbers whose squares have at least one 1 and one 2 in ternary representation.

Original entry on oeis.org

4, 5, 7, 8, 10, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84

Offset: 1

Michel Marcus, Nov 12 2012

So a(n)^2 belongs to A125293.

Complement of A176189.

K. Mahler, The representation of squares to the base 3, Acta Arith. Vol. 53, Issue 1 (1989), p. 99-106.

Cf. A125293, A176189.

Select[Range[100],DigitCount[#^2,3,1]>0&&DigitCount[#^2,3,2]>0&] (* Harvey P. Dale, May 07 2015 *)

cp's OEIS Frontend

A363408 Squares whose base-3 expansion has no 2.

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