

A053661


For n > 1: if n is present, 2n is not.


6



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, 37, 39, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 61, 63, 65, 67, 68, 69, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99, 100, 101, 103, 105
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OFFSET

1,2


COMMENTS

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
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]
Subsequence of A175880; A000040, A001749, A002001, A002042, A002063, A002089, A003947, A004171 and A081294 are subsequences.


LINKS

Robert Israel, 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.


MAPLE

N:= 1000: # to get all terms <= N
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


MATHEMATICA

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 *)


PROG

(Haskell)
a053661 n = a053661_list !! (n1)
a053661_list = filter (> 0) a175880_list  Reinhard Zumkeller, Feb 09 2011


CROSSREFS

Essentially identical to A171944 and the complement of A171945.
Sequence in context: A227802 A228856 A274688 * A171944 A134623 A228373
Adjacent sequences: A053658 A053659 A053660 * A053662 A053663 A053664


KEYWORD

nonn,easy


AUTHOR

Jeevan Chana Rai (Karanjit.Rai(AT)btinternet.com), Feb 16 2000


EXTENSIONS

More terms from James A. Sellers, Feb 22 2000


STATUS

approved



