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Search: id:A078608
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| A078608 |
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a(n) = ceiling( 2/(2^(1/n)-1)). |
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+0
4
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| 2, 5, 8, 11, 14, 17, 20, 23, 25, 28, 31, 34, 37, 40, 43, 46, 49, 51, 54, 57, 60, 63, 66, 69, 72, 75, 77, 80, 83, 86, 89, 92, 95, 98, 100, 103, 106, 109, 112, 115, 118, 121, 124, 126, 129, 132, 135, 138, 141, 144, 147, 150, 152, 155, 158, 161, 164, 167, 170, 173, 176, 178, 181
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n >= 2, a(n) = least positive integer x such that 2*x^n>(x+2)^n. For example, a(2)=5 as 4^2=16, 5^2=25, 6^2=36 and 7^2=49.
Coincides with floor( 2*n/(log 2) ) for all n from 1 to 777451915729367 but differs at 777451915729368. See A129935.
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REFERENCES
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S. W. Golomb and A. W. Hales, "Hypercube Tic-Tac-Toe", in "More Games of No Chance", ed. R. J. Nowakowski, MSRI Publications 42, Cambridge University Press, 2002, pp. 167-182. Here it is stated that the first counterexample is at n=6847196937, an error due to faulty multiprecision arithmetic. The correct value was found by J. Buhler in 2004 and is reported in S. Golomb, "Martin Gardner and Tictacktoe," in Demaine, Demaine, and Rodgers, eds., A Lifetime of Puzzles, A K Peters, 2008, pp 293-301.
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LINKS
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Authors?, Discussion in Russian
Authors?, Discussion in English
N. J. A. Sloane, Two Sequences that Agree for a Long Time (Vugraph from a talk about the OEIS)
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PROGRAM
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(PARI) for (n=2, 50, x=2; while (2*x^n<=((x+2)^n), x++); print1(x", "))
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CROSSREFS
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Cf. A078607, A078609, A129935.
Sequence in context: A140099 A109232 A064718 this_sequence A016789 A165334 A135677
Adjacent sequences: A078605 A078606 A078607 this_sequence A078609 A078610 A078611
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Dec 09 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 17 2002
Revised by N. J. A. Sloane (njas(AT)research.att.com), Jun 07 2007
Reference updated by Gerry Myerson (gerry(AT)math.mq.edu.au), Feb 08 2009
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