A246055 Denominators of the first rational corners of the function m(x) for x>=1/2.

5684610, 662, 110033282, 175783207694477729162, 234681009773714, 175771291756643579978

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. A range of x for which this conjecture is true found by Cellarosi and Munday (improving the results of Chamberland and Martelli). An explicit piecewise affine formula for m(x) is found. 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 denominators 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. A246054 (numerators).

Sequence in context: A254388 A254395 A253983 * A210353 A205045 A139064

Adjacent sequences: A246052 A246053 A246054 * A246056 A246057 A246058

Keyword

nonn,frac,more

Author

Francesco Cellarosi, Oct 06 2014

Status

approved