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A107919 Sum of terms of continued fraction for the harmonic mean of n and n-th prime. 4

%I #7 Jun 26 2022 20:04:31

%S 4,6,7,16,14,16,21,21,28,26,25,32,29,36,33,34,37,47,41,43,41,48,89,52,

%T 58,53,53,60,57,59,68,63,66,75,69,75,74,78,75,110,78,83,88,102,85,92,

%U 100,349,111,104,97,101,103,109,104,119,115,119,111,119,112,126,127,124

%N Sum of terms of continued fraction for the harmonic mean of n and n-th prime.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicMean.html">Harmonic Mean</a>.

%e a(10)=26 because the 10th prime is 29, the harmonic mean of 10 and 29 is 580/39 and the continued fraction for 580/39 has terms {14,1,6,1,4} and sum of terms 26.

%t A107919[n_]:=PLus@@ContinuedFraction[HarmonicMean[{n, Prime[n]}]]

%Y Cf. A107918.

%K nonn

%O 1,1

%A _Zak Seidov_, May 28 2005

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