Large Numbers in Some Noncomputable Sequences
The busy beaver function Σ is an example of a function which grows faster than any computable function. Its value for even relatively small input is huge. The values of Σ(n) for n = 1, 2, 3, 4 are 1, 4, 6, 13 (sequence A028444 in OEIS). Σ(5) is not known but is definitely ≥ 4098. Σ(6) is at least 3.5×1018267.
Some of the work by Harvey Friedman also involve sequences that grow faster than any computable function.
Read more about this topic: Large Numbers
Famous quotes containing the words large and/or numbers:
“Switzerland is a small, steep country, much more up and down than sideways, and is all stuck over with large brown hotels built on the cuckoo clock style of architecture.”
—Ernest Hemingway (1899–1961)
“Green grow the rushes-O
What is your one-O?”
—Unknown. Carol of the Numbers (l. 2–3)