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A074940 Numbers having at least one 2 in their ternary representation. 36

%I

%S 2,5,6,7,8,11,14,15,16,17,18,19,20,21,22,23,24,25,26,29,32,33,34,35,

%T 38,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,

%U 63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,83,86,87,88,89,92

%N Numbers having at least one 2 in their ternary representation.

%C Also, numbers n such that 3 divides C(2n,n).

%C Also, numbers n such that central trinomial coefficient A002426(n) == 0 (mod 3). - _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003

%C Also, numbers n such that A092255(n)==0 mod (3) - _Benoit Cloitre_, Mar 22 2004

%C Also, numbers n such that coefficient of x^n equals 0 in prod(k>=0, 1-x^(3^k))

%H Charles R Greathouse IV, <a href="/A074940/b074940.txt">Table of n, a(n) for n = 1..10000</a>

%H E. Deutsch and B. E. Sagan, <a href="http://arxiv.org/abs/math.CO/0407326">Congruences for Catalan and Motzkin numbers and related sequences</a>, arXiv:math/0407326 [math.CO], 2004.

%H E. Deutsch and B. E. Sagan, <a href="http://dx.doi.org/10.1016/j.jnt.2005.06.005">Congruences for Catalan and Motzkin numbers and related sequences</a>, J. Num. Theory 117 (2006), 191-215.

%F a(n) = n + O(n^0.631). [_Charles R Greathouse IV_, Aug 21 2011]

%e 12 is not in the sequence since it is 110 in base 3, but 11 is in the sequence since it is 102 in base 3 - _Michael B. Porter_, Jun 30 2016

%t Select[Range@ 120, MemberQ[IntegerDigits[#, 3], 2] &] (* or *)

%t Select[Range@ 120, Divisible[Binomial[2 #, #], 3] &] (* _Michael De Vlieger_, Jun 29 2016 *)

%t Select[Range[100],DigitCount[#,3,2]>0&] (* _Harvey P. Dale_, Aug 25 2019 *)

%o (PARI) is(n)=while(n,if(n%3==2,return(1));n\=3);0 \\ _Charles R Greathouse IV_, Aug 21 2011

%o (Haskell)

%o a074940 n = a074940_list !! (n-1)

%o a074940_list = filter ((== 0) . a039966) [0..]

%o -- _Reinhard Zumkeller_, Jun 06 2012, Sep 29 2011

%Y Complement of A005836.

%Y Cf. A006996, A007089, A081603, A081610, A081605, A081606.

%Y A039966(a(n)) = 0.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_ and _Reinhard Zumkeller_, Oct 04 2002; revised Dec 03 2003

%E More terms from _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003

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Last modified March 3 14:58 EST 2021. Contains 341762 sequences. (Running on oeis4.)