A383236 The least number of applications of Ackermann-Péter functions to reach n, starting from 0.
1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 5, 6, 7, 8, 8, 9, 9, 10, 9, 10, 10, 11, 10, 11, 11, 12, 6, 7, 8, 9, 10, 11, 11, 12, 11, 12, 12, 13, 12, 13, 13, 14, 12, 13, 13, 14, 13, 14, 14, 15, 13, 14, 14, 15, 14, 15, 15, 16, 7, 8, 9, 10
Offset: 1
Examples
For n=65533, n = A(5,0) = A(A(2,1),0) = A(A(A(0,1),A(0,0)),0) = A(A(A(0,A(0,0)),A(0,0)),0) which is a(65533) = 5 applications of A, and this is the fewest possible.
Links
- Hendrik Ballhausen, Table of n, a(n) for n = 1..2048
- Rózsa Péter, Konstruktion nichtrekursiver Funktionen, Mathematische Annalen, 111 (1935), 42-60.
- Wikipedia, Ackermann function
Formula
a(n) = min_{k,m: A(k,m)=n} a(k) + a(m) + 1
Comments