User blog comment:Edwin Shade/An Injection From The Countable Ordinals To The Reals/@comment-30754445-20171219174932/@comment-1605058-20171219180854

For ω+1, we look how many steps it takes to reduce ω+1 for a given n: we get ω+1, ω, n, n-1, ..., 2, 1, 0. so n+2 reductions. Hence Ordname(ω+1)=0.3t4t5t...