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A171947
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P-positions for game of UpMark.
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6
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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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graph;
refs;
listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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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))];
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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