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

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

Offset

1,1

Comments

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))

Links

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.

Formula

a(n) = n + O(n^0.631). [Charles R Greathouse IV, Aug 21 2011]

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

easy,nonn

Author

Benoit Cloitre and Reinhard Zumkeller, Oct 04 2002; revised Dec 03 2003

Extensions

More terms from Emeric Deutsch and Bruce E. Sagan, Dec 04 2003

Status

approved