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Search: id:A143797
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| A143797 |
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Ackermann-Buck function, defined recursively by A(0,n) = n+1, A(1,0) = 2, A(2,0) = 0, A(n+3,0) = 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, 0, 4, 4, 2, 1, 5, 5, 4, 2, 1, 6, 6, 6, 4, 2, 1, 7, 7, 8, 8, 4, 2, 1, 8, 8, 10, 16, 16, 4, 2, 1, 9, 9, 12, 32, 65536, 65536, 4, 2, 1, 10, 10, 14, 64
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OFFSET
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0,2
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COMMENT
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The next term is 2^^5 = 2^2^2^2^2 = 2^65536.
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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T(n,0) = 1 if n>=3.
T(n,1) = 2 if n>=2.
T(n,2) = 4 if n>=1.
T(1,n) = 2+n.
T(2,n) = 2*n.
T(3,n) = 2^n.
T(4,n) = 2^^n (a power tower of n two's) = A014221(n+1).
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CROSSREFS
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A001695(n)=A(n, n). Cf. A143796.
Sequence in context: A127009 A164089 A068460 this_sequence A079729 A071859 A105899
Adjacent sequences: A143794 A143795 A143796 this_sequence A143798 A143799 A143800
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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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