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Search: id:A161890
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| 0, 2, 3, 4, 6, 7, 9, 13, 15, 16, 18, 19, 20, 22, 24, 26, 27, 28, 30, 32, 34, 35, 36, 38, 39, 41, 45, 47, 48, 50, 51, 52, 54, 55, 57
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OFFSET
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0,2
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COMMENT
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Or union of transection of A161639 and {A079523(n)-8} and transection of A161673 and {A121539(n)-8}. In general, for a>=1, consider equations A010060(x+a)+A010060(x)=1, A010060(x+a)=A010060(x). Denote via B_a (C_a) the sequence of nonnegative solutions of the first (second) equation. Then we have recursions: B_(a+1) is the union of transactions 1) C_a and {A121539(n)-a}, 2) B_a and {A079523(n)-a}; C_(a+1) is the union of transactions 1) C_a and {A079523(n)-a}, 2) B_a and {A121539(n)-a}.
Conjecture. In every sequence of numbers n, such that A010060(n)=A010060(n+k), for fixed odd k, the odious (A000069) and evil (A001969) terms alternate. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jul 31 2009]
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LINKS
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V. Shevelev,Equations of the form $t(x+a)=t(x)$ and $t(x+a)=1-t(x)$ for Thue-Morse sequence [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jul 31 2009]
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CROSSREFS
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A161824 A161817 A161674 A161673 A161639 A161641 A161627 A161579 A161580 A121539 A131323 A036554 A010060 A079523 A081706
Sequence in context: A117595 A050050 A117307 this_sequence A089388 A055494 A165773
Adjacent sequences: A161887 A161888 A161889 this_sequence A161891 A161892 A161893
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 21 2009
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