Egyptian-Fraction Expansions Of REALS

[N. J. A. Sloane]

On this same thread, let me mention a potential
new sequence:  numbers n such that 1/n has
the same Engel and Sylvester expansions.

This was prompted by seeing the following paper:

MR2008063 
Wu, Jun(PRC-WUHAN) 
How many points have the same Engel and Sylvester expansions? (English. English summary) 
J. Number Theory 103 (2003), no. 1, 16--26.

which computes the Hausdorff dimension of these
points (without giving any examples)

(cf. A048860, A005832, etc., A054543, etc.)

It might be an interesting task to investigate these numbers.

NJAS