Question: In the lanthanide series, how many members must there be?
About the article "Atomic number", section "Moseley's 1913 experiment".

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The results of the increased attraction of the outer shell electrons across the lanthanide period may be divided into effects on the lanthanide series itself including the decrease in ionic radii, and influences on the following or post-lanthanide elements. 
When in the form of coordination complexes, lanthanides exist overwhelmingly in their +3 oxidation state, although particularly stable 4f configurations can also give +4 (Ce, Tb) or +2 (Eu, Yb) ions.
All of these forms are strongly electropositive and thus lanthanide ions are hard Lewis acids.
The oxidation states are also very stable and with the exception of SmI2 and cerium(IV) salts lanthanides are not used for redox chemistry.
4f electrons have a high probability of being found close to the nucleus and are thus strongly affected as the nuclear charge increases across the series; this results in a corresponding decrease in ionic radii referred to as the lanthanide contraction.
The low probability of the 4f electrons existing at the outer region of the atom or ion permits little effective overlap between the orbitals of a lanthanide ion and any binding ligand.
Thus lanthanide complexes typically have little or no covalent character and are not influenced by orbital geometries.
The lack of orbital interaction also means that varying the metal typically has little effect on the complex (other than size), especially when compared to transition metals.
Complexes are held together by weaker electrostatic forces which are omni-directional and thus the ligands alone dictate the symmetry and coordination of complexes.
Steric factors therefore dominate, with coordinative saturation of the metal being balanced against inter-ligand repulsion.
This results in a diverse range of coordination geometries, many of which are irregular, and also manifests itself in the highly fluxional nature of the complexes.
As there is no energetic reason to be locked into a single geometry rapid intramolecular and intermolecular ligand exchange will take place, which typically results in complexes which will rapidly fluctuate between all possible configurations.
Many of these features make lanthanide complexes effective catalysts.
Hard Lewis acids are able to polarise bonds upon coordination and thus alter the electrophilicity of compounds, with a classic example being the Luche reduction.
The large size of the ions coupled with their labile ionic bonding allows even bulky coordinating species to bind and dissociate rapidly, resulting in very high turnover rates; thus excellent yields can often be achieved with loadings of only a few mol%.
The lack of orbital interactions combined with the lanthanide contraction means that the lanthanides change in size across the series but that their chemistry remains much the same.
This allows for easy tuning of the steric environments and examples exist where this has been used to improve the catalytic activity of the complex and change the nuclearity of metal clusters.
Despite this, the use of lanthanide coordination complexes as homogeneous catalysts is largely restricted to the laboratory and there are currently few examples them being used on an industrial scale.
It should be noted however, that lanthanides exist in many forms other that coordination complexes and many of these are industrially useful.
In particular lanthanide metal oxides are used as heterogeneous catalysts in various industrial processes. 
The ionic radii of the lanthanides decrease from 103 pm (La3+) to 86 pm (Lu3+) in the lanthanide series.
Across the lanthanide series, electrons are added to the "4f" shell.
This first "f" shell is inside the full "5s" and "5p" shells (as well as the "6s" shell in the neutral atom); the "4f" shell is well-localized near the atomic nucleus and has little effect on chemical bonding.
The decrease in atomic and ionic radii does affect their chemistry, however.
Without the lanthanide contraction, a chemical separation of lanthanides would be extremely difficult.
However, this contraction makes the chemical separation of period 5 and period 6 transition metals of the same group rather difficult.
There is a general trend of increasing Vickers hardness, Brinell hardness, density and melting point from lanthanum to lutetium (with ytterbium being the most notable exception).
Lutetium is the hardest and densest lanthanide and has the highest melting point. 
Lanthanide triflates can be convenient anhydrous precursors to many bis(trimethylsilyl)amides:  Ln(OTf)3 + 3 M(hmds) → Ln(hmds)3 + 3 MOTf (M = Li, Na, K; Ln = La, Nd, Sm, Er) However it is more common to see the preparation of lanthanide bis(trimethylsilyl)amides from anhydrous lanthanide chlorides, as these are cheaper.
The reaction is performed in THF and requires a period at reflux.
Once formed, the product is separated from LiCl by exchanging the solvent for toluene, in which Ln(hmds)3 is soluble but LiCl is not.
Ln(Cl)3 + 3 HMDS + 3 nBuLi → Ln(hmds)3 + 3 LiCl + 3 butane (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Ho, Yb, and Lu) Silylamides are important as starting materials in lanthanide chemistry, as lanthanide chlorides have either poor solubility or poor stability in common solvents.
As a result of this nearly all lanthanide silylamides are commercially available.
There has also been some success in the synthesis and characterization of actinide bis(trimethylsilyl)amides.
A convenient synthetic route uses the THF-adducts of the iodide salts AnI3(THF)4 as starting materials. 
The lanthanide or lanthanoid series of chemical elements comprises the fifteen metallic chemical elements with atomic numbers 57 through 71, from lanthanum through lutetium.
These fifteen lanthanide elements, along with the chemically similar elements scandium and yttrium, are often collectively known as the rare earth elements.
The informal chemical symbol Ln is used in general discussions of lanthanide chemistry to refer to any lanthanide.
All but one of the lanthanides are f-block elements, corresponding to the filling of the 4f electron shell; lutetium, a d-block element, is also generally considered to be a lanthanide due to its chemical similarities with the other fourteen.
All lanthanide elements form trivalent cations, Ln3+, whose chemistry is largely determined by the ionic radius, which decreases steadily from lanthanum to lutetium.
The lanthanide elements are the group of elements with atomic number increasing from 57 (lanthanum) to 71 (lutetium).
They are termed lanthanide because the lighter elements in the series are chemically similar to lanthanum.
Strictly speaking, both lanthanum and lutetium have been labeled as group 3 elements, because they both have a single valence electron in the d shell.
However, both elements are often included in any general discussion of the chemistry of the lanthanide elements.
In presentations of the periodic table, the lanthanides and the actinides are customarily shown as two additional rows below the main body of the table, with placeholders or else a selected single element of each series (either lanthanum and actinium, or lutetium and lawrencium) shown in a single cell of the main table, between barium and hafnium, and radium and rutherfordium, respectively.
This convention is entirely a matter of aesthetics and formatting practicality; a rarely used wide-formatted periodic table inserts the lanthanide and actinide series in their proper places, as parts of the table's sixth and seventh rows (periods).