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

%I A081606 #32 Oct 29 2024 12:39:55
%S A081606 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 A081606 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,55,57,
%U A081606 58,59,61,63,64,65,66,67,68,69,70,71,73,75,76,77,79,81,82,83,84,85,86
%N A081606 Numbers having at least one 1 in their ternary representation.
%C A081606 Complement of A005823.
%C A081606 Integers m such that central Delannoy number A001850(m) == 0 (mod 3). - _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003
%C A081606 Integers m such that A026375(m) == 0 (mod 3). - _Fabio Visonà_, Aug 03 2023
%H A081606 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 A081606 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 A081606 Select[Range[100],DigitCount[#,3,1]>0&] (* _Harvey P. Dale_, Nov 26 2022 *)
%o A081606 (Python)
%o A081606 from itertools import count, islice
%o A081606 def A081606_gen(): # generator of terms
%o A081606     a = 0
%o A081606     for n in count(1):
%o A081606         b = int(bin(n)[2:],3)<<1
%o A081606         yield from range(a+1,b)
%o A081606         a = b
%o A081606 A081606_list = list(islice(A081606_gen(),30)) # _Chai Wah Wu_, Oct 13 2023
%o A081606 (Python)
%o A081606 from gmpy2 import digits
%o A081606 def A081606(n):
%o A081606     def f(x):
%o A081606         s = digits(x>>1,3)
%o A081606         for i in range(l:=len(s)):
%o A081606             if s[i]>'1':
%o A081606                 break
%o A081606         else:
%o A081606             return n+int(s,2)
%o A081606         return n-1+(int(s[:i] or '0',2)+1<<l-i)
%o A081606     m, k = n, f(n)
%o A081606     while m != k: m, k = k, f(k)
%o A081606     return m # _Chai Wah Wu_, Oct 29 2024
%Y A081606 Cf. A007089, A062756, A081609, A081605, A074940.
%K A081606 nonn,base
%O A081606 1,2
%A A081606 _Reinhard Zumkeller_, Mar 23 2003
%E A081606 More terms from _Emeric Deutsch_ and _Bruce E. Sagan_, Dec 04 2003