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Search: id:A164657
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| A164657 |
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Denominators of partial sums of Theta(5):=sum(1/(2*j-1)^5,j=1..infty). |
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3
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| 1, 243, 759375, 12762815625, 3101364196875, 499477805270915625, 185452612752454075153125, 185452612752454075153125, 263316190384861185784690603125, 651996955695764397260286617707209375, 651996955695764397260286617707209375, 4196476041813743307955464949873473110315625
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The numerators are given by A164656.
For a reference and a W. Lang link see A164656.
Rationals (partial sums) Theta(5,n) := sum(1/(2*j-1)^5,j=1..n) (in lowest terms). The limit of these rationals is Theta(5)= (1-1/2^5)*Zeta(5) approximately 1.004523763 (Zeta(n) is the Euler, Riemann Zeta function).
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FORMULA
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a(n) = denominator(Theta(5,n))= numerator(sum(1/(2*j-1)^5,j=1..n)), n>=1.
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EXAMPLE
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Rationals Theta(5,n): [1, 244/243, 762743/759375, 12820180976/12762815625, 3115356499043/3101364196875,...].
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CROSSREFS
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Sequence in context: A017309 A017429 A017561 this_sequence A151638 A051002 A044987
Adjacent sequences: A164654 A164655 A164656 this_sequence A164658 A164659 A164660
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang@physik.uni-karlsruhe.de) Oct 16 2009
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