This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A176189 #16 Jun 08 2023 02:04:25 %S A176189 1,2,3,6,9,11,16,18,19,27,29,33,48,54,55,57,81,83,87,99,143,144,162, %T A176189 163,165,171,243,245,249,261,262,297,421,429,432,451,486,487,489,495, %U A176189 513,729,731,735,747,783,786,889,891,1263,1287,1296,1331,1342,1353,1458 %N A176189 Natural numbers whose squares have only 0's and 1's in base 3. %C A176189 If 3 divides a(n) then a(n)/3 also appears in this sequence. Also the inverse is true: if a(n) appears, then (3^k)*a(n), for all k>=0, appears as well. %C A176189 Note that a(n) usually does not consist only of 0's and 1's - it can be shown that in this case a(n)=3^k, for some k>=0. %C A176189 So, a(n)^2 belongs to A005836. - _Michel Marcus_, Nov 12 2012 %H A176189 Alois P. Heinz, <a href="/A176189/b176189.txt">Table of n, a(n) for n = 1..1000</a> %H A176189 K. Mahler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa53/aa5316.pdf">The representation of squares to the base 3</a>, Acta Arith. Vol. 53, Issue 1 (1989), p. 99-106. %e A176189 For n=16 we have 16^2=256="100111" (in base 3). Also (16*3)^2="10011100", (16*3^2)^2="1001110000", etc. %t A176189 Select[Range[1200], Max[IntegerDigits[ #^2, 3]] == 1 &] %o A176189 (Python) %o A176189 from gmpy2 import digits %o A176189 def ok(n): return "2" not in digits(n*n, 3) %o A176189 print([k for k in range(1, 1500) if ok(k)]) # _Michael S. Branicky_, Jun 07 2023 %Y A176189 Cf. A005836. %K A176189 base,easy,nonn %O A176189 1,2 %A A176189 _Maciej Ireneusz Wilczynski_, Apr 11 2010