Q:

List of proteins by number of amino acids / chain length

Is there any protein database online where I could obtain a list of proteins ordered by the length of their chains / number of amino acids, starting from the shortest, as well as to see their amino acid sequences?
I'd like to start from the short & simple protein structures to see how their particular sequences of amino acids translate into their folding shape, and what those short chains are capable of doing in organisms. (I heard about the LILs, but they are artificially-generated and consist of just two amino acids, Lysine and Isoleucine, so not much variety to study in there :q )
But I'm quite new to these databases, they present a lot of details, but usually not the one I'm looking for, and one has to know what too look for first to get any meaningful information :q

A:

You can find the data you need in the Protein Data Bank.

Since 1971, the Protein Data Bank archive (PDB) has served as the
  single repository of information about the 3D structures of proteins,
  nucleic acids, and complex assemblies.
The Worldwide PDB (wwPDB) organization manages the PDB archive and
  ensures that the PDB is freely and publicly available to the global
  community.

Each of the PDB member organisations provides the same data with a different interface:

PDBe,
PDBj,
RCSB.

In general, you either query the database through one of the web interfaces, or you download all the data and search it locally. In this case, the RCSB website has the option you asked about (sorting by the residue count):

Alternatively, you could download:
ftp://ftp.wwpdb.org/pub/pdb/derived_data/pdb_seqres.txt
and parse it and sort it as you wish.
This file has sequences of all chains in the PDB entries.
But since your goal is to find the relationship between the sequence and the folded structure, you should probably start from reading about the protein folding problem and about methods used in protein structure prediction.

A:

In the UniProt Knowledgebase, you can have your proteins sorted by protein length, e.g. in this query for all human proteins with a cross-reference to PDB:
https://www.uniprot.org/uniprot/?query=database%3A(type%3Apdb)%20AND%20organism%3A%22Homo%20sapiens%20(Human)%20%5B9606%5D%22&columns=id%2Centry%20name%2Creviewed%2Cprotein%20names%2Cgenes%2Clength&sort=length
Default sorting is by query score, but if you click on the black triangles in the table headings, e.g. for sequence length, you can have them sorted by other criteria.

