

A176189


Natural numbers whose squares have only 0's and 1's in base 3.


1



1, 2, 3, 6, 9, 11, 16, 18, 19, 27, 29, 33, 48, 54, 55, 57, 81, 83, 87, 99, 143, 144, 162, 163, 165, 171, 243, 245, 249, 261, 262, 297, 421, 429, 432, 451, 486, 487, 489, 495, 513, 729, 731, 735, 747, 783, 786, 889, 891
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OFFSET

1,2


COMMENTS

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.
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.
So, a(n)^2 belongs to A005836.  Michel Marcus, Nov 12 2012


LINKS

Table of n, a(n) for n=1..49.
K. Mahler, The representation of squares to the base 3, Acta Arith. Vol. 53, Issue 1 (1989), p. 99106.


EXAMPLE

For n=16 we have 16^2=256="100111" (in base 3). Also (16*3)^2="10011100", (16*3^2)^2="1001110000", etc.


MATHEMATICA

Select[Range[1200], Max[IntegerDigits[ #^2, 3]] == 1 &]


CROSSREFS

Cf. A005836.
Sequence in context: A067886 A227000 A338546 * A057127 A224449 A007780
Adjacent sequences: A176186 A176187 A176188 * A176190 A176191 A176192


KEYWORD

base,easy,nonn


AUTHOR

Maciej Ireneusz Wilczynski, Apr 11 2010


STATUS

approved



