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A363408 Squares whose base-3 expansion has no 2.

%I A363408 #15 Jun 11 2023 14:17:14
%S A363408 0,1,4,9,36,81,121,256,324,361,729,841,1089,2304,2916,3025,3249,6561,
%T A363408 6889,7569,9801,20449,20736,26244,26569,27225,29241,59049,60025,62001,
%U A363408 68121,68644,88209,177241,184041,186624,203401,236196,237169,239121,245025,263169,531441,534361,540225,558009
%N A363408 Squares whose base-3 expansion has no 2.
%C A363408 Squares that are the sum of distinct powers of 3.
%C A363408 If k is a term, then so is 9*k.
%C A363408 The only square whose base-3 expansion has no 1 is 0.
%H A363408 Robert Israel, <a href="/A363408/b363408.txt">Table of n, a(n) for n = 1..665</a>
%F A363408 a(n) = A176189(n-1)^2 for n>=2. - _Alois P. Heinz_, Jun 07 2023
%e A363408 a(5) = 36 is a term because 36 = 6^2 = 3^2 + 3^3.
%p A363408 R:= {0,1};
%p A363408 S:= {1};
%p A363408 for i from 1 to 20 do
%p A363408   S:= map(t -> (3*t, 3*t+1), S);
%p A363408   R:= R union select(issqr,S)
%p A363408 od:
%p A363408 R;
%t A363408 Select[Range[0, 1000]^2, ! MemberQ[IntegerDigits[#, 3], 2] &] (* _Amiram Eldar_, Jun 01 2023 *)
%o A363408 (Python)
%o A363408 from gmpy2 import digits
%o A363408 def okA176189(n): return "2" not in digits(n*n, 3)
%o A363408 print([k**2 for k in range(1000) if okA176189(k)]) # _Michael S. Branicky_, Jun 07 2023
%Y A363408 Intersection of A000290 and A005836. Cf. A363428.
%Y A363408 Cf. A176189.
%K A363408 nonn,base
%O A363408 1,3
%A A363408 _Robert Israel_, May 31 2023