

A246054


Numerators of the first rational corners of the meanmedian map limit value m(x) for x >= 1/2.


1




OFFSET

1,1


COMMENTS

The function m(x) is the limit value of the meanmedian map. Start with 0<x<1 and find a new number x_4 so that the median of {0,x,1} equals the mean of {0,x,1,x_4}. Then find a new number x_5 so that the median of {0,x,1,x_4} equals the mean of {0,x,1,x_4,x_5}, etc. It is conjectured by Shultz and Shiflett that for all real x this process ends after finitely many steps. Cellarosi and Munday find a range of x for which this conjecture is true (improving results of Chamberland and Martelli), and an explicit piecewise affine formula for m(x). It is enough to study the case of 1/2 <= x <= 2/3. The first rational corners of the map m(x) to the right of 1/2 are found by Cellarosi and Munday and these are the rationals whose numerators are listed above.


LINKS

M. Chamberland, and M. Martelli, The meanmedian map, Journal of Difference Equations and Applications 13, 577583 (2007)
H. Shultz, and R. Shiflett, M&m Sequences, The College Mathematics Journal 36, Number 3, 2005.


CROSSREFS



KEYWORD

nonn,frac,more


AUTHOR



STATUS

approved



