A246054 Numerators of the first rational corners of the mean-median map limit value m(x) for x >= 1/2.

2911001, 339, 56346353, 90028408624696264845, 120193266020529, 90022305806716382445

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