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A171947
P-positions for game of UpMark.
6
1, 3, 7, 9, 11, 15, 19, 23, 25, 27, 31, 33, 35, 39, 41, 43, 47, 51, 55, 57, 59, 63, 67, 71, 73, 75, 79, 83, 87, 89, 91, 95, 97, 99, 103, 105, 107, 111, 115, 119, 121, 123, 127, 129, 131, 135, 137, 139, 143, 147, 151, 153, 155, 159, 161, 163, 167, 169, 171, 175, 179
OFFSET
1,2
COMMENTS
The following description, due to D. R. Hofstadter, Email, Oct 23 2014, is presumably equivalent to Fraenkel's. Begin with 1, and then each new member is 2k-1, where k is the smallest unused non-member of the sequence. Thus k starts out as 2, so 2k-1 = 3, so 3 is the sequence's second member. The next value of k is 4, giving 2k-1 = 7, so 7 is the sequence's third member. Then k = 5, so 9 is the next member. Then k = 6, so 11 is the next member. Then k = 8, so 15 is the next member. Etc. - N. J. A. Sloane, Oct 26 2014
It appears that this is the sequence of positions of 1 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 0 in the limiting 0-word of the morphism 0->11, 1-> 01. See A285383. - Clark Kimberling, Apr 26 2017
It appears that this sequence gives integers that are congruent to 2^k+1 (mod 2^(k+1)), where k is any odd integer >=1. - Jules Beauchamp, Dec 04 2023
LINKS
Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 42-46.
FORMULA
Presumably equal to 2*A003159 + 1. - Reinhard Zumkeller, Oct 26 2014
MAPLE
# Maple code for M+1 terms of sequence, from N. J. A. Sloane, Oct 26 2014
m:=1; a:=[m]; M:=100;
for n from 1 to M do
m:=m+1; if m in a then m:=m+1; fi;
c:=2*m-1;
a:=[op(a), c];
od:
[seq(a[n], n=1..nops(a))];
MATHEMATICA
f[n_] := Block[{a = {1}, b = {}, k}, Do[k = 2; While[MemberQ[a, k] || MemberQ[b, k], k++]; AppendTo[a, 2 k - 1]; AppendTo[b, k], {i, 2, n}]; a]; f@ 120 (* Michael De Vlieger, Jul 20 2015 *)
PROG
(Haskell)
import Data.List (delete)
a171947 n = a171947_list !! (n-1)
a171947_list = 1 : f [2..] where
f (w:ws) = y : f (delete y ws) where y = 2 * w - 1
-- Reinhard Zumkeller, Oct 26 2014
CROSSREFS
Complement of A171946. Essentially identical to A072939.
A249034 gives missing odd numbers.
Cf. A003159.
Sequence in context: A359567 A125667 A072939 * A287914 A291348 A186890
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 29 2010
STATUS
approved