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A100398 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.

%I A100398 #20 Feb 16 2025 08:32:55
%S A100398 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,
%T A100398 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,
%U A100398 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
%N A100398 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.
%C A100398 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_, May 31 2008
%H A100398 M. F. Hasler, <a href="/A100398/b100398.txt">Table of n, a(n) for n=1..105013</a>.
%H A100398 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%H A100398 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>
%e A100398 Since the 3rd harmonic number is 11/6 = 1 +1/(1 +1/5), the 3rd row is 1,1,5.
%t A100398 Flatten[Table[ContinuedFraction[HarmonicNumber[n]], {n, 16}]] (* _Ray Chandler_, Sep 17 2005 *)
%o A100398 (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
%Y A100398 m-th harmonic number H(m) = A001008(m)/A002805(m).
%Y A100398 Cf. A055573, A058027, A110020, A112286, A112287.
%K A100398 nonn,tabl
%O A100398 1,3
%A A100398 _Leroy Quet_, Dec 30 2004
%E A100398 Extended by _Ray Chandler_, Sep 17 2005