A107928 - OEIS

%I #13 Mar 11 2014 19:53:49

%S 2,3,12,24,16,96,192,128,768,1536,1024,6144,12288,8192,49152,98304,

%T 65536,393216,786432,524288,3145728,6291456,4194304,25165824,50331648,

%U 33554432,201326592,402653184,268435456,1610612736

%N a(n) is the numerator of harmonic mean of a(n-1) and a(n-2).

%F a(1)=2; a(2)=3; n>=3: a(n) = numerator(2*a(n-1)*a(n-2)/(a(n-2)+a(n-1))).

%F Conjecture: G.f.: x*(2+3*x+12*x^2+8*x^3+8*x^4)/[(1-2*x)*(1+2*x+4*x^2)]. a(3n) = (3/2)*8^n, a(3n+1) = 3*8^n, a(3n+2) = 2*8^n, for n>0. - _Ralf Stephan_, Dec 01 2010

%t a[1]=2;a[2]=3;a[n_]:=a[n]=Numerator[HarmonicMean[{a[n-1], a[n-2]}]];

%t nxt[{a_,b_}]:={b,Numerator[HarmonicMean[{a,b}]]}; Transpose[ NestList[nxt,{2,3},30]][[1]] (* _Harvey P. Dale_, Jul 25 2013 *)

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Jun 10 2005