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 A171947 P-positions for game of UpMark. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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 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. 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: A047529 A125667 A072939 * A287914 A186890 A248667 Adjacent sequences:  A171944 A171945 A171946 * A171948 A171949 A171950 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Oct 29 2010 STATUS approved

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