

A100398


Array where nth row (of A055573(n) terms) is the continued fraction terms for the nth harmonic number, sum{ k=1 to n} 1/k.


12



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
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OFFSET

1,3


COMMENTS

Terms corresponding to H(n) (i.e. the nth row) end at index A139001(n)=sum(i=1..n,A055573(n))  M. F. Hasler, May 31 2008


LINKS

M. F. Hasler, Table of n, a(n) for n=1..105013.
Eric Weisstein's World of Mathematics, Harmonic Number
Eric Weisstein's World of Mathematics, Continued Fraction


EXAMPLE

Since the 3rd harmonic number is 11/6 = 1 +1/(1 +1/5), the 3rd row is 1,1,5.


MATHEMATICA

Flatten[Table[ContinuedFraction[HarmonicNumber[n]], {n, 16}]] (* Ray Chandler, Sep 17 2005 *)


PROG

(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, May 31 2008


CROSSREFS

mth harmonic number H(m) = A001008(m)/A002805(m).
Cf. A055573, A058027, A110020, A112286, A112287.
Sequence in context: A003570 A011281 A300731 * A160364 A107735 A137570
Adjacent sequences: A100395 A100396 A100397 * A100399 A100400 A100401


KEYWORD

nonn,tabl


AUTHOR

Leroy Quet, Dec 30 2004


EXTENSIONS

Extended by Ray Chandler, Sep 17 2005


STATUS

approved



