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Search: id:A014221
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| A014221 |
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a(0) = 0; for n >= 0, a(n+1) = 2^a(n). This is the Ackermann function A_3(n+1) as defined in the Comments line.. |
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32
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OFFSET
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0,3
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COMMENT
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Next term has 19729 digits - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 28 2002
Harvey Friedman defines the Ackermann function as follows: A_1(n) = 2n, A_{k+1}(n) = A_k A_k ... A_k(1), where there are n A_k's. A_2(n) = 2^n.
Harvey Friedman's rapidly increasing sequence 3, 11, huge, ... does not fit into the constraints of the OEIS. It is described in the paper "Long finite sequences". The third term is > A_7198(158386), which is incomprehensibly huge. See also the Gijswijt article.
The Goodstein sequence described in the Comments in A056041 grows even faster than Friedman's.
a(n) is the smallest a(n-1)-almost prime for n >= 2; e.g. a(5) = 65536 = A069277(1) (smallest (a(4)=16)-almost prime). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 28 2006
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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.
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LINKS
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W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99 (1928), 118-133.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
H. M. Friedman, Long finite sequences, J. Comb. Theory, A 95 (2001), 102-144.
H. M. Friedman, Long finite sequences, J. Comb. Theory, A 95 (2001), 102-144. [A faster site] [Link may be broken]
D. Gijswijt, Een onvoorstelbaar lang woord [An unimaginably long word]
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing (arXiv:math.NT/0611293).
Robert P. Munafo, Sequence A094358, 2^^N = 1 mod N.
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FORMULA
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a(n+1) = 2^a(n), where a(0)=0. - Daniel B. Cristofani (cristofd(AT)hevanet.com), Apr 02 2003
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CROSSREFS
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Cf. A038081, A001695, A046859, A093382.
Cf. A115658 (a(n) is the smallest square-free a(n-1)-almost prime).
Sequence in context: A114641 A001128 A124436 this_sequence A048872 A105510 A118242
Adjacent sequences: A014218 A014219 A014220 this_sequence A014222 A014223 A014224
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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