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Search: id:A056054
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| A056054 |
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a(n) = smallest even number 2m such that value of odd harmonic series Sum_{j=0..m} 1/(2j) is > n. |
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+0
5
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| 8, 62, 454, 3348, 24734, 182760, 1350428, 9978382, 73730824, 544801200, 4025566630, 29745137662, 219788490858, 1624029488844, 12000044999386, 88669005690160, 655180257281000, 4841163675961122, 35771629985782052
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers 2*m such that floor(f(m))=floor(f(m-1)) where f(m)= Sum_{j=1..m} ((2*j-1)/(2*j)). Examples: floor(f(1))=floor(1/2)=0; floor(f(2))=floor(1/2+2/3)=floor(1,25)=1, then 2*2=4 is not in the sequence; floor(f(3))=floor((1/2+3/4+4/5)=floor(2,083..)=2, then 2*3=6 is not in the sequence; floor((f(4))=floor(1/2+3/4+5/6+7/8)=floor(2,958..)=2, then 2*4=8 is the first term of the sequence. - Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Aug 15 2007
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REFERENCES
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Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Plenum Press, NY and London, 1996, page 64.
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FORMULA
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a(n) = 2*A002387(2n).
The next term is approximately the previous term * e^2.
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MATHEMATICA
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s = 0; k = 2; Do[ While[s = N[s + 1/k, 24]; s <= n, k += 2]; Print[k]; k += 2, {n, 1, 12}]
(* or assuming that the Mathematica coding in A002387 is correct then *)
b[n_] := Module[{k = Floor[2a[2n]]}, If[ EvenQ[k], k, k + 1]]; Table[ b[n], {n, 19}] (from Robert G. Wilson v Apr 17 2004)
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CROSSREFS
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Cf. A002387, A056053, A091463, A091464, A091465.
Cf. A056054.
Sequence in context: A001466 A082179 A044527 this_sequence A126628 A085353 A125396
Adjacent sequences: A056051 A056052 A056053 this_sequence A056055 A056056 A056057
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 25 2000 and Jan 11 2004
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