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A143796
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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).
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2
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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
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OFFSET
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0,2
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COMMENTS
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Also known as Ackermann-Peter function.
The next term is 2^65536-3.
This is a computable function that is not primitive recursive.
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REFERENCES
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R. Peter, Rekursive Funktionen in der Komputer-Theorie. Budapest: Akad. Kiado, 1951.
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LINKS
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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.
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FORMULA
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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).
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Benoit Jubin, Sep 01 2008
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STATUS
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approved
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