A171946 - OEIS

%I #29 Jan 29 2025 19:59:48

%S 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 38,40,42,44,45,46,48,49,50,52,53,54,56,58,60,61,62,64,65,66,68,69,70,

%U 72,74,76,77,78,80,81,82,84,85,86,88,90,92,93,94,96,98

%N N-positions for game of UpMark.

%C 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 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 Apparently a(n) = 1+A003159(n-1). - _R. J. Mathar_, Jun 24 2021

%H Reinhard Zumkeller, <a href="/A171946/b171946.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 (Haskell)

%o import Data.List (delete)

%o a171946 n = a171946_list !! (n-1)

%o a171946_list = 0 : f [2..] where

%o    f (w:ws) = w : f (delete (2 * w - 1) ws)

%o -- _Reinhard Zumkeller_, Oct 26 2014

%o (Python)

%o def A171946(n):

%o     if n == 1: return 0

%o     def f(x):

%o         c, s = n, bin(x-1)[2:]

%o         l = len(s)

%o         for i in range(l&1,l,2):

%o             c += int(s[i])+int('0'+s[:i],2)

%o         return c

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Jan 29 2025

%Y Complement of A171947.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Oct 29 2010