

A078608


a(n) = ceiling(2/(2^(1/n)1)).


6



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
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OFFSET

1,1


COMMENTS

For n >= 2, a(n) is the 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.
The first few values of n for which this sequence differs from floor( 2*n/(log 2) ) were found by Dean Hickerson in 2002.  N. J. A. Sloane, Apr 30 2014
The sequence floor( log(n)/(2*log(2)) ) is mentioned by Erdős and Selfridge (1973). This sequence begins 0,0,0,1,1,1,1,... = 0 (3 times), 1 (12 times), 2 (48 times), 3 (192 times), 4 (768 times), ..., and grows too slowly to have its own entry. It is related to the game studied by Hales and Jewett (1963).  N. J. A. Sloane, Dec 02 2016


REFERENCES

S. Golomb, "Martin Gardner and Tictacktoe," in Demaine, Demaine, and Rodgers, eds., A Lifetime of Puzzles, A K Peters, 2008, pp. 293301.
S. W. Golomb and A. W. Hales, "Hypercube TicTacToe", in "More Games of No Chance", ed. R. J. Nowakowski, MSRI Publications 42, Cambridge University Press, 2002, pp. 167182. 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 Dean Hickerson in 2002, and J. Buhler in 2004, and is reported in S. Golomb (2008).
Dean Hickerson, Email to Jon Perry and N. J. A. Sloane, Dec 16 2002. Gives first three terms of A129935: 777451915729368, 140894092055857794, 1526223088619171207, as well as five later terms.  N. J. A. Sloane, Apr 30 2014


LINKS

Max Alekseyev and others, Integer Parts [in Russian] [Cached copy in pdf format]
Paul Erdős and John L. Selfridge, On a combinatorial game, Journal of Combinatorial Theory, Series A 14.3 (1973): 298301.


MATHEMATICA



PROG

(PARI) for (n=2, 50, x=2; while (2*x^n<=((x+2)^n), x++); print1(x", "))
(Haskell)
a078608 = ceiling . (2 /) . (subtract 1) . (2 **) . recip . fromIntegral


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



