Create Custom Content Type using Client Object Model

It's not possible to set the content type id in CSOM. Not sure why the difference. The closest you can get is setting the ParentContentType value, but that leaves the final two digits to be randomly generated. This is how to create a content type in CSOM:

var clientContext = new ClientContext( siteUrl );
// For SharePoint Online
var credentials = new SharePointOnlineCredentials(login, secureStringPassword);
clientContext.Credentials = credentials;

var contentTypes = clientContext.Web.ContentTypes;
var contentTypeCreationInformation = new ContentTypeCreationInformation
                                     {
                                         Name = "Content Type Name",
                                         Description = "Description",
                                         Group = "Group",
                                         ParentContentType = ContentType // Must be content type object
                                     };
var contentType = contentTypes.Add( contentTypeCreationInformation );
clientContext.Load( contentType );
clientContext.ExecuteQuery();
clientContext.Dispose();