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Search: id:A100398
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| A100398 |
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Array where n-th row (of A055573(n) terms) is the continued fraction terms for the n-th harmonic number, sum{ k=1 to n} 1/k. |
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+0
11
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| 1, 1, 2, 1, 1, 5, 2, 12, 2, 3, 1, 1, 8, 2, 2, 4, 2, 2, 1, 1, 2, 5, 5, 2, 1, 2, 1, 1, 5, 7, 2, 1, 4, 1, 5, 1, 1, 7, 1, 3, 2, 1, 13, 12, 1, 3, 1, 2, 3, 50, 3, 4, 6, 1, 5, 3, 9, 1, 2, 4, 1, 1, 1, 15, 4, 3, 5, 1, 1, 4, 2, 1, 3, 2, 1, 3, 1, 4, 1, 6, 3, 3, 1, 39, 3, 1, 13, 3, 13, 3, 3, 7, 43, 1, 1, 1, 17, 7, 3, 2
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Terms corresponding to H(n) (i.e. the n-th row) end at index A139001(n)=sum(i=1..n,A055573(n)) - M. F. Hasler (www.univ-ag.fr/~mhasler), May 31 2008
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LINKS
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M. F. Hasler, Table of n, a(n) for n=1,...,105013.
Leroy Quet, Home Page (listed in lieu of email address)
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Continued Fraction
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EXAMPLE
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Since the 3rd harmonic number is 11/6 = 1 +1/(1 +1/5), the 3rd row is 1,1,5.
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MATHEMATICA
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Flatten[Table[ContinuedFraction[HarmonicNumber[n]], {n, 16}]] (*Chandler*)
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PROGRAM
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(PARI) c=0; h=0; for(n=1, 500, for(i=1, #t=contfrac(h+=1/n), write("b100398.txt", c++, " ", t[i]))) - M. F. Hasler (www.univ-ag.fr/~mhasler), May 31 2008
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CROSSREFS
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m-th harmonic number H(m) = A001008(m)/A002805(m).
Cf. A055573, A058027, A110020, A112286, A112287.
Sequence in context: A075259 A003570 A011281 this_sequence A160364 A107735 A137570
Adjacent sequences: A100395 A100396 A100397 this_sequence A100399 A100400 A100401
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet, Dec 30 2004
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 17 2005
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