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Search: id:A079523
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| A079523 |
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Numbers n such that binary representation ends in an odd number of ones. |
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+0
27
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| 1, 5, 7, 9, 13, 17, 21, 23, 25, 29, 31, 33, 37, 39, 41, 45, 49, 53, 55, 57, 61, 65, 69, 71, 73, 77, 81, 85, 87, 89, 93, 95, 97, 101, 103, 105, 109, 113, 117, 119, 121, 125, 127, 129, 133, 135, 137, 141, 145, 149, 151, 153, 157, 159, 161, 165, 167, 169, 173, 177, 181
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OFFSET
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1,2
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COMMENT
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Also, n such that A010060(n)=A010060(n+1) where A010060 is the Thue-Morse sequence.
Sequence of n such that a(n)=3n begins 7, 23, 27, 29, 31, 39, 71, 87, 91, 93, 95, ...
Values of k such that the Motzkin number A001006(2k) is even. Values of k such that the number of restricted hexagonal polyominoes with 2k+1 cells is even (see A002212). Values of k such that the number of directed animals of size k+1 is even (see A005773). Values of k such that the Riordan number A005043(k) is even. - Emeric Deutsch (deutsch(AT)duke.poly.edu) and Bruce E. Sagan, Apr 02 2003
a(n) = A036554(n)-1 = A072939(n)-2. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 09 2003
Odious and evil terms alternate. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 22 2009]
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REFERENCES
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J.-P. Allouche, A. Arnold, J. Berstel, S. Brlek, W. Jockusch, S. Plouffe, B. E. Sagan, A relative of the Thue-Morse sequence, Discrete Math., 139, 1995, 455-461.
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FORMULA
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a(n) is asymptotic to 3n.
a(n)=2*A003159(n)-1. a(1)=1, a(n)=a(n-1)+2 if (a(n-1)+1)/2 does not belong to the sequence and a(n)=a(n-1)+4 otherwise. - Emeric Deutsch (deutsch(AT)duke.poly.edu) and Bruce E. Sagan, Apr 02 2003
a(n)=(1/2)A081706(2n-1).
a(n) = A003158(n) - n = A003157(n) - n - 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 22 2004
Values of k such that A091297(k) = 0 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 25 2004
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CROSSREFS
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Cf. A003159.
Cf. A003157 A003158 A003159.
Sequence in context: A089193 A111083 A050550 this_sequence A039504 A097280 A155732
Adjacent sequences: A079520 A079521 A079522 this_sequence A079524 A079525 A079526
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 21 2003
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