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A171946 N-positions for game of UpMark.

%I A171946 #29 Jan 29 2025 19:59:48
%S A171946 0,2,4,5,6,8,10,12,13,14,16,17,18,20,21,22,24,26,28,29,30,32,34,36,37,
%T A171946 38,40,42,44,45,46,48,49,50,52,53,54,56,58,60,61,62,64,65,66,68,69,70,
%U A171946 72,74,76,77,78,80,81,82,84,85,86,88,90,92,93,94,96,98
%N A171946 N-positions for game of UpMark.
%C A171946 It appears that this is the sequence of positions of 0 in the 1-limiting word of the morphism 0 -> 10, 1 -> 00; see A284948. - _Clark Kimberling_, Apr 18 2017
%C A171946 It appears that this sequence gives the positions of 1 in the limiting 0-word of the morphism 0->11, 1-> 01.  See A285383.  - _Clark Kimberling_, Apr 26 2017
%C A171946 Apparently a(n) = 1+A003159(n-1). - _R. J. Mathar_, Jun 24 2021
%H A171946 Reinhard Zumkeller, <a href="/A171946/b171946.txt">Table of n, a(n) for n = 1..10000</a>
%H A171946 Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1016/j.disc.2011.03.032">The vile, dopey, evil and odious game players</a>, Discrete Math. 312 (2012), no. 1, 42-46.
%o A171946 (Haskell)
%o A171946 import Data.List (delete)
%o A171946 a171946 n = a171946_list !! (n-1)
%o A171946 a171946_list = 0 : f [2..] where
%o A171946    f (w:ws) = w : f (delete (2 * w - 1) ws)
%o A171946 -- _Reinhard Zumkeller_, Oct 26 2014
%o A171946 (Python)
%o A171946 def A171946(n):
%o A171946     if n == 1: return 0
%o A171946     def f(x):
%o A171946         c, s = n, bin(x-1)[2:]
%o A171946         l = len(s)
%o A171946         for i in range(l&1,l,2):
%o A171946             c += int(s[i])+int('0'+s[:i],2)
%o A171946         return c
%o A171946     m, k = n, f(n)
%o A171946     while m != k: m, k = k, f(k)
%o A171946     return m # _Chai Wah Wu_, Jan 29 2025
%Y A171946 Complement of A171947.
%K A171946 nonn,easy
%O A171946 1,2
%A A171946 _N. J. A. Sloane_, Oct 29 2010