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Search: id:A143796
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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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+0
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
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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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.
R. Peter, Rekursive Funktionen in der Komputer-Theorie. Budapest: Akad. Kiado, 1951.
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LINKS
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Wikipedia, Ackermann function.
E. Weisstein, Mathworld, 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: A107347 A163127 A077113 this_sequence A057362 A085269 A054071
Adjacent sequences: A143793 A143794 A143795 this_sequence 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 (benoit_jubin(AT)yahoo.fr), Sep 01 2008
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