MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
show/hide this revision's text 2 added 1 characters in body

You might take a look at the paper by Forenc Adorjan, "Binary Mappings of montonic monotonic sequences and the Aronson function". It specifically discusses the number you describe.
show/hide this revision's text 1

You might take a look at the paper by Forenc Adorjan, "Binary Mappings of montonic sequences and the Aronson function". It specifically discusses the number you describe.