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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 The correct value was found by J. Buhler in 2004 and is reported in S. Golomb, "Martin Gardner and Tictacktoe" (unpublished).
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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 A135677 A000093
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(AT)math.ucdavis.edu), Dec 17 2002
Revised by njas, Jun 07 2007
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