|
| |
|
|
A246054
|
|
Numerators of the first rational corners of the mean-median map limit value m(x) for x >= 1/2.
|
|
1
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The function m(x) is the limit value of the mean-median 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
|
Table of n, a(n) for n=1..6.
F. Cellarosi, S. Munday, On two conjectures for M&m sequences, arXiv:1408.3454 [math.CO], 2014.
M. Chamberland, and M. Martelli, The mean-median map, Journal of Difference Equations and Applications 13, 577--583 (2007)
H. Shultz, and R. Shiflett, M&m Sequences, The College Mathematics Journal 36, Number 3, 2005.
|
|
|
CROSSREFS
|
Cf. A246055 (denominators).
Sequence in context: A101769 A237210 A209795 * A251247 A205292 A205900
Adjacent sequences: A246051 A246052 A246053 * A246055 A246056 A246057
|
|
|
KEYWORD
|
nonn,frac,more
|
|
|
AUTHOR
|
Francesco Cellarosi, Aug 12 2014
|
|
|
STATUS
|
approved
|
| |
|
|
