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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 29 2010
STATUS
approved