This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053661 #35 Jul 02 2025 16:01:59
%S A053661 1,2,3,5,7,8,9,11,12,13,15,17,19,20,21,23,25,27,28,29,31,32,33,35,36,
%T A053661 37,39,41,43,44,45,47,48,49,51,52,53,55,57,59,60,61,63,65,67,68,69,71,
%U A053661 73,75,76,77,79,80,81,83,84,85,87,89,91,92,93,95,97,99,100,101,103,105
%N A053661 For n > 1: if n is present, 2n is not.
%C A053661 The Name line gives a property of the sequence, not a definition. The sequence can be defined simultaneously with b(n) := A171945(n) via a(n) = mex{a(i), b(i) : 0 <= i < n} (n >= 0}, b(n)=2a(n). The two sequences are complementary, hence A053661 is identical to A171944 (except for the first terms). Furthmore, A053661 is the same as A003159 except for the replacement of vile by dopey powers of 2. - _Aviezri S. Fraenkel_, Apr 28 2011
%C A053661 For n >= 2, either n = 2^k where k is odd or n = 2^k*m where m > 1 is odd and k is even (found by Kirk Bresniker and Stan Wagon). [_Robert Israel_, Oct 10 2010]
%C A053661 Subsequence of A175880; A000040, A001749, A002001, A002042, A002063, A002089, A003947, A004171 and A081294 are subsequences.
%H A053661 Robert Israel, <a href="/A053661/b053661.txt">Table of n, a(n) for n = 1..10000</a>
%H A053661 Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1016/j.disc.2011.03.032">The vile, dopey, evil and odious game players</a>, Discrete Math. 312 (2012), no. 1, 42-46.
%p A053661 N:= 1000: # to get all terms <= N
%p A053661 sort([1,seq(2^(2*i+1),i=0..(ilog2(N)-1)/2), seq(seq(2^(2*i)*(2*j+1),j=1..(N/2^(2*i)-1)/2),i=0..ilog2(N)/2)]); # _Robert Israel_, Jul 24 2015
%t A053661 Clear[T]; nn = 105; T[n_, k_] := T[n, k] = If[n < 1 || k < 1, 0, If[n == 1 || k == 1, 1, If[k > n, T[k, n], If[n > k, T[k, Mod[n, k, 1]], -Product[T[n, i], {i, n - 1}]]]]]; DeleteCases[Table[If[T[n, n] == -1, n, ""], {n, 1, nn}], ""] (* _Mats Granvik_, Aug 25 2012 *)
%o A053661 (Haskell)
%o A053661 a053661 n = a053661_list !! (n-1)
%o A053661 a053661_list = filter (> 0) a175880_list -- _Reinhard Zumkeller_, Feb 09 2011
%Y A053661 Essentially identical to A171944 and the complement of A171945.
%K A053661 nonn,easy
%O A053661 1,2
%A A053661 Jeevan Chana Rai (Karanjit.Rai(AT)btinternet.com), Feb 16 2000
%E A053661 More terms from _James Sellers_, Feb 22 2000