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A004231
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Ackermann's sequence: n^^n := n^n^n^...^n (with n n's).
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2
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OFFSET
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0,3
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COMMENTS
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Using Knuth's arrow notation, this is n^^^2 (n-penta-2) or n^^n (n-tetra-n). - Andrew Robbins, Apr 16 2009
Comment from Trevor Green (green(AT)dlcwest.com): The fourth term in this sequence has about as many digits - 8.07 * 10^153 - as the *square* of the number of protons in the universe.
We could prepend a(0) = 1 (since 0^^0 = 1, that is, the "empty power tower" gives the "empty product"). - Daniel Forgues, May 17 2013
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REFERENCES
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W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99 (1928), 118-133.
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LINKS
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Table of n, a(n) for n=0..3.
Eric Weisstein's World of Mathematics, Ackermann Number
Wikipedia, Knuth's up-arrow notation
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CROSSREFS
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Cf. A027747, A008868 (which mentions an older estimate for the same number).
Sequence in context: A161405 A147876 A164796 * A066546 A132653 A115544
Adjacent sequences: A004228 A004229 A004230 * A004232 A004233 A004234
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KEYWORD
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nonn,bref,changed
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AUTHOR
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wild(AT)edumath.u-strasbg.fr (Daniel Wild)
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STATUS
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approved
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