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%I #28 Jun 11 2022 05:24:19
%S 1,3,9,13,27,31,37,39,81,85,91,93,109,111,117,121,243,247,253,255,271,
%T 273,279,283,325,327,333,337,351,355,361,363,729,733,739,741,757,759,
%U 765,769,811,813,819,823,837,841,847,849,973,975,981,985,999,1003,1009
%N Odd numbers such that base 3 representation contains no 2.
%C Odd numbers in A005836.
%C Numbers m such that coefficient of x^m equals -1 in Product_{k>=0} 1-x^(3^k).
%C Numbers k such that binomial(2k, k) == 2 (mod 3).
%C Sum of an odd number of distinct powers of 3. - _Emeric Deutsch_, Dec 03 2003
%H Amiram Eldar, <a href="/A074938/b074938.txt">Table of n, a(n) for n = 0..10000</a>
%H Emeric Deutsch and B. E. Sagan, <a href="https://arxiv.org/abs/math/0407326">Congruences for Catalan and Motzkin numbers and related sequences</a>, arXiv:math/0407326 [math.CO], 2004; J. Num. Theory 117 (2006), 191-215.
%F a(n) (mod 3) = A010059(n).
%F ((a(n)-1)/2) (mod 3) = A010060(n) = (1/2)*{binomial(2*a(n)+1, a(n)) (mod 3)}.
%t Select[Range[1,1111,2],Count[IntegerDigits[#,3],2]==0&] (* _Harvey P. Dale_, Dec 19, 2010 *)
%Y Intersection of A005408 and A005836.
%Y Cf. A006996, A074939.
%K easy,nonn
%O 0,2
%A _Benoit Cloitre_, Oct 04 2002; Nov 15 2003
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