login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Denominator of the harmonic mean of the first n positive Fibonacci numbers.
3

%I #14 Aug 31 2020 16:40:56

%S 1,1,5,17,91,379,721,35849,614893,6800951,607326679,3651532639,

%T 851897554247,24724573280923,301787157353771,14188276949397301,

%U 22662903194758542865,430644772287132696121,1800653989272587268758525,369150309888695460837999593

%N Denominator of the harmonic mean of the first n positive Fibonacci numbers.

%C Similar to A059248. - _Michel Marcus_ and _Colin Barker_, Nov 28 2014

%H Colin Barker, <a href="/A250744/b250744.txt">Table of n, a(n) for n = 1..120</a>

%e a(4) = 17 because the first 4 positive Fibonacci numbers are [1,1,2,3], and 4/(1/1+1/1+1/2+1/3) = 24/17.

%t Module[{nn=20,f},f=Fibonacci[Range[nn]];Table[HarmonicMean[Take[f,n]],{n,nn}]]//Denominator (* _Harvey P. Dale_, Aug 31 2020 *)

%o (PARI) s=vector(30); f=Vec(x/(1-x-x^2)+O(x^(#s+1))); n=d=0; for(k=1, #s, n++; d+=1/f[k]; s[k]=denominator(n/d)); s

%Y Cf. A000045 (Fibonacci numbers), A250743 (numerators).

%Y Cf. A059248.

%K nonn,frac

%O 1,3

%A _Colin Barker_, Nov 27 2014