A081606 Numbers having at least one 1 in their ternary representation.

1, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 84, 85, 86

Offset: 1

Author

Reinhard Zumkeller, Mar 23 2003

Keywords

• nonn
• base

Comments

Complement of A005823.

Integers m such that central Delannoy number A001850(m) == 0 (mod 3). - Emeric Deutsch and Bruce E. Sagan, Dec 04 2003

Integers m such that A026375(m) == 0 (mod 3). - Fabio Visonà, Aug 03 2023

Links

• Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p.25.
• Mathematics Stack Exchange, Proof that integers m in this sequence are such that A026375(m) == 0 (mod 3).

Crossrefs

Cf. A007089, A062756, A081609, A081605, A074940.

Programs

Mathematica

Select[Range[100],DigitCount[#,3,1]>0&] (* Harvey P. Dale, Nov 26 2022 *)

Python

from itertools import count, islice
def A081606_gen(): # generator of terms
    a = 0
    for n in count(1):
        b = int(bin(n)[2:],3)<<1
        yield from range(a+1,b)
        a = b
A081606_list = list(islice(A081606_gen(),30)) # Chai Wah Wu, Oct 13 2023

Python

from gmpy2 import digits
def A081606(n):
    def f(x):
        s = digits(x>>1,3)
        for i in range(l:=len(s)):
            if s[i]>'1':
                break
        else:
            return n+int(s,2)
        return n-1+(int(s[:i] or '0',2)+1<Chai Wah Wu, Oct 29 2024

Extensions

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