The On-Line Encyclopedia of Integer Sequences (OEIS)

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A107919

Sum of terms of continued fraction for the harmonic mean of n and n-th prime.
(history; published version)

#7 by Wesley Ivan Hurt at Sun Jun 26 20:04:31 EDT 2022

STATUS

editing

approved

#6 by Wesley Ivan Hurt at Sun Jun 26 20:04:21 EDT 2022

COMMENTS

Cf. A107918

EXAMPLE

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.

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 17:26:16 EDT 2012

AUTHOR

_Zak Seidov (zakseidov(AT)yahoo.com), _, May 28 2005

Discussion

Fri Mar 30

17:26

OEIS Server: https://oeis.org/edit/global/139

#4 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

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

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

LINKS

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

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

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

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

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

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

DATA

4, 6, 7, 16, 14, 16, 21, 21, 28, 26, 25, 32, 29, 36, 33, 34, 37, 47, 41, 43, 41, 48, 89, 52, 58, 53, 53, 60, 57, 59, 68, 63, 66, 75, 69, 75, 74, 78, 75, 110, 78, 83, 88, 102, 85, 92, 100, 349, 111, 104, 97, 101, 103, 109, 104, 119, 115, 119, 111, 119, 112, 126, 127, 124

OFFSET

1,1

COMMENTS

Cf. A107918

LINKS

Eric W. Weisstein, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>.

Eric W. Weisstein, <a href="http://mathworld.wolfram.com/HarmonicMean.html">Harmonic Mean</a>.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A107918.

KEYWORD

nonn

AUTHOR

Zak Seidov (zakseidov(AT)yahoo.com), May 28 2005

STATUS

approved