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A166871 Permutation of the integers: 3 positives, 2 negatives. 3


%S 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,

%T 16,17,18,-11,-12,19,20,21,-13,-14,22,23,24,-15,-16,25,26,27,-17,-18,

%U 28,29,30,-19,-20,31,32,33,-21,-22,34,35,36,-23,-24,37,38,39,-25,-26,40,41

%N Permutation of the integers: 3 positives, 2 negatives.

%C This sequence enumerates the denominators with sign in case p=3 and n=2 of:

%C 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) )

%C 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.

%C Case p=2, n=1 is A166711.

%C Case p=1, n=1 is A001057.

%H G. C. Greubel, <a href="/A166871/b166871.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Riemann_series_theorem">Riemann series theorem</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,2,0,0,0,0,-1)

%F Sum_{k>0} 1/a(k) = log(3/2).

%F G.f.: x*(1+2*x+3*x^2-x^3-2*x^4+2*x^5+x^6-x^8)/((x-1)^2*(x^4+x^3+x^2+x+1)^2 ).

%t LinearRecurrence[{0,0,0,0,2,0,0,0,0,-1},{0,1,2,3,-1,-2,4,5,6,-3}, 100] (* _G. C. Greubel_, May 27 2016 *)

%Y Cf. A016578, A166711.

%K sign,easy

%O 0,3

%A _Jaume Oliver Lafont_, Oct 22 2009

%E keyword frac removed _Jaume Oliver Lafont_, Nov 02 2009

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Last modified February 19 18:22 EST 2019. Contains 320327 sequences. (Running on oeis4.)