%I #32 Oct 29 2024 12:39:55
%S 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,
%T 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,55,57,
%U 58,59,61,63,64,65,66,67,68,69,70,71,73,75,76,77,79,81,82,83,84,85,86
%N Numbers having at least one 1 in their ternary representation.
%C Complement of A005823.
%C Integers m such that central Delannoy number A001850(m) == 0 (mod 3). - _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003
%C Integers m such that A026375(m) == 0 (mod 3). - _Fabio VisonĂ _, Aug 03 2023
%H Johann Cigler, <a href="https://arxiv.org/abs/1611.05252">Some elementary observations on Narayana polynomials and related topics</a>, arXiv:1611.05252 [math.CO], 2016. See p.25.
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/a/4746447/573047">Proof that integers m in this sequence are such that A026375(m) == 0 (mod 3)</a>.
%t Select[Range[100],DigitCount[#,3,1]>0&] (* _Harvey P. Dale_, Nov 26 2022 *)
%o (Python)
%o from itertools import count, islice
%o def A081606_gen(): # generator of terms
%o a = 0
%o for n in count(1):
%o b = int(bin(n)[2:],3)<<1
%o yield from range(a+1,b)
%o a = b
%o A081606_list = list(islice(A081606_gen(),30)) # _Chai Wah Wu_, Oct 13 2023
%o (Python)
%o from gmpy2 import digits
%o def A081606(n):
%o def f(x):
%o s = digits(x>>1,3)
%o for i in range(l:=len(s)):
%o if s[i]>'1':
%o break
%o else:
%o return n+int(s,2)
%o return n-1+(int(s[:i] or '0',2)+1<<l-i)
%o m, k = n, f(n)
%o while m != k: m, k = k, f(k)
%o return m # _Chai Wah Wu_, Oct 29 2024
%Y Cf. A007089, A062756, A081609, A081605, A074940.
%K nonn,base
%O 1,2
%A _Reinhard Zumkeller_, Mar 23 2003
%E More terms from _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003