The th Takeuchi number is the value of the function which measures how many times the Takeuchi function has to call itself to give the answer starting with . For example, the second Takeuchi number is 4, since requires four recursions to obtain the answer 2. The first few Takeuchi numbers are 0, 1, 4, 14, 53, 223, 1034, 5221, 28437, listed in A000651 of Sloane’s OEIS. Prellberg gives a formula for the asymptotic growth of the Takeuchi numbers:
, where is the Takeuchi-Prellberg constant (approximately 2.2394331), is the th Bernoulli number and is Lambert’s function.
|Date of creation||2013-03-22 17:33:09|
|Last modified on||2013-03-22 17:33:09|
|Last modified by||PrimeFan (13766)|