A series is called artistic if every three consecutive terms have a common three-way ratio
![P[a_i,a_(i+1),a_(i+2)]=((a_i+a_(i+1)+a_(i+2))a_(i+1))/(a_ia_(i+2)).](/images/equations/ArtisticSequence/NumberedEquation1.svg) |
A series is also artistic iff its series bias is a constant. A geometric
series with ratio 
is an artistic series with
 |
Artistic Sequence
See also
Geometric Series, Melodic Sequence, Series BiasExplore with Wolfram|Alpha
References
Duffin, R. J. "On Seeing Progressions of Constant Cross Ratio." Amer. Math. Monthly 100, 38-47, 1993.Referenced on Wolfram|Alpha
Artistic SequenceCite this as:
Weisstein, Eric W. "Artistic Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArtisticSequence.html