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Search: id:A082968
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| A082968 |
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a(n)=sum(k=1,n, k modulo(sum(i=0,k-1,1-t(i))) where t(i)=A010060(i) is the Thue-Morse sequence. |
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+0
1
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| 0, 0, 0, 0, 1, 1, 4, 4, 5, 5, 10, 10, 16, 16, 17, 17, 18, 18, 27, 27, 37, 37, 38, 38, 50, 50, 51, 51, 52, 52, 67, 67, 68, 68, 85, 85, 103, 103, 104, 104, 124, 124, 125, 125, 126, 126, 149, 149, 173, 173, 174, 174, 175, 175, 202, 202, 203, 203, 232, 232, 262, 262, 263, 263
(list; graph; listen)
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OFFSET
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1,7
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FORMULA
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Despite the definition, a(n) has an unexpectedly simple asymptotic behavior h: a(n)=(n/4)^2 +O(n) and more precisely it appears that : (n/4)^2-n/8 <= a(n) < (n/4)^2+n/2 with equality (on left side) for infinetely many values of n.
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PROGRAM
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(PARI) a(n)=sum(k=1, n, k%sum(i=0, k-1, 1-subst(Pol(binary(i)), x, 1)%2))
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CROSSREFS
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Sequence in context: A065864 A120205 A152465 this_sequence A136013 A114884 A132704
Adjacent sequences: A082965 A082966 A082967 this_sequence A082969 A082970 A082971
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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), May 27 2003
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