

A171947


Ppositions for game of UpMark.


4



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
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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 2k1, where k is the smallest unused nonmember of the sequence. Thus k starts out as 2, so 2k1 = 3, so 3 is the sequence's second member. The next value of k is 4, giving 2k1 = 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 1limiting 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 0word of the morphism 0>11, 1> 01. See A285383.  Clark Kimberling, Apr 26 2017


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, 4246.


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*m1;
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 !! (n1)
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: A047529 A125667 A072939 * A186890 A248667 A075607
Adjacent sequences: A171944 A171945 A171946 * A171948 A171949 A171950


KEYWORD

nonn,easy,changed


AUTHOR

N. J. A. Sloane, Oct 29 2010


STATUS

approved



