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A074940
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Numbers having at least one 2 in their ternary representation.
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36
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2, 5, 6, 7, 8, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 32, 33, 34, 35, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 86, 87, 88, 89, 92
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OFFSET
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1,1
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COMMENTS
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Also, numbers n such that 3 divides C(2n,n).
Also, numbers n such that central trinomial coefficient A002426(n) == 0 (mod 3). - Emeric Deutsch and Bruce E. Sagan, Dec 04 2003
Also, numbers n such that A092255(n)==0 mod (3) - Benoit Cloitre, Mar 22 2004
Also, numbers n such that coefficient of x^n equals 0 in prod(k>=0, 1-x^(3^k))
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, arXiv:math/0407326 [math.CO], 2004.
E. Deutsch and B. E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.
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FORMULA
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a(n) = n + O(n^0.631). [Charles R Greathouse IV, Aug 21 2011]
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EXAMPLE
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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
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MATHEMATICA
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Select[Range@ 120, MemberQ[IntegerDigits[#, 3], 2] &] (* or *)
Select[Range@ 120, Divisible[Binomial[2 #, #], 3] &] (* Michael De Vlieger, Jun 29 2016 *)
Select[Range[100], DigitCount[#, 3, 2]>0&] (* Harvey P. Dale, Aug 25 2019 *)
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PROG
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(PARI) is(n)=while(n, if(n%3==2, return(1)); n\=3); 0 \\ Charles R Greathouse IV, Aug 21 2011
(Haskell)
a074940 n = a074940_list !! (n-1)
a074940_list = filter ((== 0) . a039966) [0..]
-- Reinhard Zumkeller, Jun 06 2012, Sep 29 2011
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CROSSREFS
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Complement of A005836.
Cf. A006996, A007089, A081603, A081610, A081605, A081606.
A039966(a(n)) = 0.
Sequence in context: A275894 A299635 A170944 * A028752 A028791 A080727
Adjacent sequences: A074937 A074938 A074939 * A074941 A074942 A074943
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre and Reinhard Zumkeller, Oct 04 2002; revised Dec 03 2003
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EXTENSIONS
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More terms from Emeric Deutsch and Bruce E. Sagan, Dec 04 2003
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STATUS
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approved
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