A171946 N-positions for game of UpMark.

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, 38, 40, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 58, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96, 98

Offset

1,2

Comments

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

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

Apparently a(n) = 1+A003159(n-1). - R. J. Mathar, Jun 24 2021

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 42-46.

Prog

(Haskell)
import Data.List (delete)
a171946 n = a171946_list !! (n-1)
a171946_list = 0 : f [2..] where
   f (w:ws) = w : f (delete (2 * w - 1) ws)
-- Reinhard Zumkeller, Oct 26 2014
(Python)
def A171946(n):
    if n == 1: return 0
    def f(x):
        c, s = n, bin(x-1)[2:]
        l = len(s)
        for i in range(l&1, l, 2):
            c += int(s[i])+int('0'+s[:i], 2)
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jan 29 2025

Crossrefs

Complement of A171947.

Sequence in context: A284818 A192584 A337140 * A285385 A026435 A026437

Adjacent sequences: A171943 A171944 A171945 * A171947 A171948 A171949

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 29 2010

Status

approved