%I A078608
%S A078608 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,
%T A078608 75,77,80,83,86,89,92,95,98,100,103,106,109,112,115,118,121,124,126,129,
%U A078608 132,135,138,141,144,147,150,152,155,158,161,164,167,170,173,176,178,181
%N A078608 a(n) = ceiling( 2/(2^(1/n)-1)).
%C A078608 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.
%C A078608 Coincides with floor( 2*n/(log 2) ) for all n from 1 to 777451915729367 
               but differs at 777451915729368. See A129935.
%D A078608 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.
%H A078608 Authors?, <a href="http://lib.mexmat.ru/forum/viewtopic.php?t=6838">Discussion 
               in Russian</a>
%H A078608 Authors?, <a href="http://www.mathlinks.ro/Forum/viewtopic.php?t=140737">
               Discussion in English</a>
%H A078608 N. J. A. Sloane, <a href="a078608.jpg">Two Sequences that Agree for a 
               Long Time</a> (Vugraph from a talk about the OEIS)
%o A078608 (PARI) for (n=2,50, x=2; while (2*x^n<=((x+2)^n),x++); print1(x","))
%Y A078608 Cf. A078607, A078609, A129935.
%Y A078608 Sequence in context: A140099 A109232 A064718 this_sequence A016789 A165334 
               A135677
%Y A078608 Adjacent sequences: A078605 A078606 A078607 this_sequence A078609 A078610 
               A078611
%K A078608 nonn
%O A078608 1,1
%A A078608 Jon Perry (perry(AT)globalnet.co.uk), Dec 09 2002
%E A078608 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 17 2002
%E A078608 Revised by N. J. A. Sloane (njas(AT)research.att.com), Jun 07 2007
%E A078608 Reference updated by Gerry Myerson (gerry(AT)math.mq.edu.au), Feb 08 
               2009