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Search: id:A166871
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| A166871 |
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Permutation of the integers: 3 positives, 2 negatives. |
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+0
3
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| 0, 1, 2, 3, -1, -2, 4, 5, 6, -3, -4, 7, 8, 9, -5, -6, 10, 11, 12, -7, -8, 13, 14, 15, -9, -10, 16, 17, 18, -11, -12, 19, 20, 21, -13, -14, 22, 23, 24, -15, -16, 25, 26, 27, -17, -18, 28, 29, 30, -19, -20, 31, 32, 33, -21, -22, 34, 35, 36, -23, -24, 37, 38, 39, -25, -26, 40, 41
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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sum(k>0,1/a(k)) = log(3/2)
This sequence enumerates the denominators with sign in case p=3 and n=2 of
log(p/n) = sum( i>=0 , sum(p*i+1<=j<=p*(i+1),1/j) - sum(n*i+1<=j<=n*(i+1),1/j) )
Similar sequences can be constructed for the logarithm of any rational r=p/n (p,n>0), enumerating p positive integers and n negative integers every p+n terms.
Case p=2, n=1 is A166711.
Case p=1, n=1 is A001057.
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LINKS
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Wikipedia, Riemann series theorem [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 01 2009]
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FORMULA
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G.f.: x*(1+2*x+3*x^2-x^3-2*x^4+2*x^5+x^6-x^8)/(1-x^5)^2
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CROSSREFS
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Cf. A016578, A166711.
Sequence in context: A048232 A163256 A144962 this_sequence A152736 A139246 A131227
Adjacent sequences: A166868 A166869 A166870 this_sequence A166872 A166873 A166874
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KEYWORD
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sign,new
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 22 2009
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EXTENSIONS
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keyword frac removed Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 02 2009
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