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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Comment from Aviezri Fraenkel, Apr 28 2011: 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.

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, 42-46.

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 !! (n-1)

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

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Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)