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A143796 Ackermann function, defined recursively by A(0,n) = n+1, A(m+1,0) = A(m,1), A(m+1,n+1) = A(m,A(m+1,n)) for any nonnegative integers n, m. Table read by antidiagonals, the second term being A(0,1). 2
1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 7, 13, 13, 6, 6, 9, 29, 65533, 65533, 7, 7, 11, 61 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also known as Ackermann-Peter function.

The next term is 2^65536-3.

This is a computable function that is not primitive recursive.

REFERENCES

R. Peter, Rekursive Funktionen in der Komputer-Theorie. Budapest: Akad. Kiado, 1951.

LINKS

Table of n, a(n) for n=0..24.

W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99 (1928), 118-133.

R. C. Buck, Mathematical induction and recursive definitions, Amer. Math. Monthly, 70 (1963), 128-135.

E. Weisstein, Mathworld, Ackermann function.

Wikipedia, Ackermann function.

FORMULA

A(1,n) = 2+(n+3) - 3 = n + 2.

A(2,n) = 2*(n+3) - 3 = 2n + 3.

A(3,n) = 2^(n+3) - 3.

A(4,n) = 2^^(n+3)- 3 (a power tower of n+3 two's).

CROSSREFS

A046859(n)=A(n, n), A126333(n)=A(n, 0). Cf. A143797.

Sequence in context: A274533 A163127 A077113 * A245473 A306904 A057362

Adjacent sequences:  A143793 A143794 A143795 * A143797 A143798 A143799

KEYWORD

nonn,tabl

AUTHOR

Benoit Jubin, Sep 01 2008

STATUS

approved

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Last modified May 24 07:31 EDT 2022. Contains 354005 sequences. (Running on oeis4.)