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

Author

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

Keywords

• easy
• nonn

Comments

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

Also, numbers m such that the central trinomial coefficient A002426(m) == 0 (mod 3). - Emeric Deutsch and Bruce E. Sagan, Dec 04 2003

Also, numbers m such that A092255(m) == 0 (mod 3). - Benoit Cloitre, Mar 22 2004

Also, numbers m such that the coefficient of x^m equals 0 in Product_{k>=0} (1-x^(3^k)). - N. J. A. Sloane, Jun 01 2010

Examples

			12 is not in the sequence since it is 110_3, but 11 is in the sequence since it is 102_3. - _Michael B. Porter_, Jun 30 2016
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Emeric Deutsch and Bruce E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, arXiv:math/0407326 [math.CO], 2004.
• Emeric Deutsch and Bruce E. Sagan, Congruences for Catalan and Motzkin numbers and related sequences, J. Num. Theory 117 (2006), 191-215.

Crossrefs

Complement of A005836.

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

A039966(a(n)) = 0.

Programs

Haskell

a074940 n = a074940_list !! (n-1)
a074940_list = filter ((== 0) . a039966) [0..]
-- Reinhard Zumkeller, Jun 06 2012, Sep 29 2011

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 *)

PARI

is(n)=while(n,if(n%3==2,return(1));n\=3);0 \\ Charles R Greathouse IV, Aug 21 2011

Python

from gmpy2 import digits
def A074940(n):
    def f(x):
        s = digits(x,3)
        for i in range(l:=len(s)):
            if s[i]>'1':
                break
        else:
            return n+int(s,2)
        return n+int(s[:i]+'1'*(l-i),2)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Oct 29 2024

Formula

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

Extensions

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