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Search: id:A027763
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| A027763 |
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Smallest k such that 2^^n is not congruent to 2^^(n-1) mod k, where 2^^n denotes the power tower 2^2^...^2 (in which 2 appears n times). |
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+0
1
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| 2, 3, 5, 11, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 531441, 1594323
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence shares many terms with A056637, the least prime of class n-. Note that 3^(n-1) is an upper bound for each term and the upper bound is reached for n=12 and n=13. Are all subsequent terms 3^(n-1)? The Mathematica code uses the TowerMod function in the CRT package, which is described in the book by Bressoud and Wagon. [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
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REFERENCES
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Stan Wagon (WAGON(AT)macalester.edu), posting to Problem of the Week mailing list, Dec 15 1997.
David Bressoud and Stan Wagon, A Course in Computational Number Theory, Key College Pub., 2000, p. 96. [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
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LINKS
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Stan Wagon, Putnam Problem Notes [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
Eric W. Weisstein, MathWorld: Power Tower [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
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EXAMPLE
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2^^2=2^2=4 and 2^^3=2^2^2=16. We find 4 = 16 (mod k) until k=5. So a(3)=5. [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
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MATHEMATICA
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Needs["CRT`"]; k=1; Table[While[TowerMod[2, n, k]==TowerMod[2, n-1, k], k++ ]; k, {n, 10}] [From T. D. Noe (noe(AT)sspectra.com), Mar 13 2009]
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CROSSREFS
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Sequence in context: A079848 A073434 A162278 this_sequence A060696 A000628 A006888
Adjacent sequences: A027760 A027761 A027762 this_sequence A027764 A027765 A027766
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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EXTENSIONS
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Improved the name and changed the offset because I just prepended a term T. D. Noe (noe(AT)sspectra.com), Mar 13 2009
Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Mar 13 2009
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