A107928 a(n) is the numerator of harmonic mean of a(n-1) and a(n-2).

2, 3, 12, 24, 16, 96, 192, 128, 768, 1536, 1024, 6144, 12288, 8192, 49152, 98304, 65536, 393216, 786432, 524288, 3145728, 6291456, 4194304, 25165824, 50331648, 33554432, 201326592, 402653184, 268435456, 1610612736

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Formula

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

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

Mathematica

a[1]=2; a[2]=3; a[n_]:=a[n]=Numerator[HarmonicMean[{a[n-1], a[n-2]}]];
nxt[{a_, b_}]:={b, Numerator[HarmonicMean[{a, b}]]}; Transpose[ NestList[nxt, {2, 3}, 30]][[1]] (* Harvey P. Dale, Jul 25 2013 *)

Crossrefs

Sequence in context: A323111 A302545 A320173 * A130337 A293697 A084728

Adjacent sequences: A107925 A107926 A107927 * A107929 A107930 A107931

Keyword

easy,nonn

Author

Zak Seidov, Jun 10 2005

Status

approved