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Search: id:A061168
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| 0, 1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 28, 31, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Given a term b>0 of the sequence and its left hand neighbour c, the corresponding unique sequence index n with property a(n)=b can be determined by n(b)=e+(b-d*(e+1)+2*(e-1))/d, where d=b-c and e=2^d. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 05 2006
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REFERENCES
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M. Griffiths, Double sequences of positive integers, Math. Gaz., 86 (2002), 285-287.
D. E. Knuth, Fundamental Algorithms, Addison-Wesley, 1973, Section 1.2.4, ex. 42(b).
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LINKS
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J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197, ex. 27.
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FORMULA
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a(n) = Sum_{k=1..n} floor(log_2(k)) = (n+1)*floor(log_2(n)) - 2*(2^floor(log_2(n)) - 1). - Diego Torres (torresvillarroel(AT)hotmail.com), Oct 29 2002
G.f.: 1/(1-x)^2 * Sum(k>=1, x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 13 2002
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MAPLE
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[seq(add(floor(log_2(k)), k=1..j), j=1..100)]
(PARI) a(n)=if(n<1, 0, if(n%2==0, a(n/2)+a(n/2-1)+n-1, 2*a((n-1)/2)+n-1)) (from R. Stephan)
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PROGRAM
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(PARI) a(n)=local(k); if(n<1, 0, k=length(binary(n))-1; (n+1)*k-2*(2^k-1))
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CROSSREFS
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Cf. A001855.
a(n) = A001855(n+1)-n.
Sequence in context: A053044 A129011 A130174 this_sequence A130798 A025224 A096182
Adjacent sequences: A061165 A061166 A061167 this_sequence A061169 A061170 A061171
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Apr 19 2001
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