

A166871


Permutation of the integers: 3 positives, 2 negatives.


3



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
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OFFSET

0,3


COMMENTS

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.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Wikipedia, Riemann series theorem
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,1)


FORMULA

Sum_{k>0} 1/a(k) = log(3/2).
G.f.: x*(1+2*x+3*x^2x^32*x^4+2*x^5+x^6x^8)/((x1)^2*(x^4+x^3+x^2+x+1)^2 ).


MATHEMATICA

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 *)


CROSSREFS

Cf. A016578, A166711.
Sequence in context: A244567 A254112 A249111 * A275728 A152736 A139246
Adjacent sequences: A166868 A166869 A166870 * A166872 A166873 A166874


KEYWORD

sign,easy


AUTHOR

Jaume Oliver Lafont, Oct 22 2009


EXTENSIONS

keyword frac removed Jaume Oliver Lafont, Nov 02 2009


STATUS

approved



