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A002379
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Floor(3^n/2^n).
(Formerly M0666 N0245)
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79
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1, 1, 2, 3, 5, 7, 11, 17, 25, 38, 57, 86, 129, 194, 291, 437, 656, 985, 1477, 2216, 3325, 4987, 7481, 11222, 16834, 25251, 37876, 56815, 85222, 127834, 191751, 287626, 431439, 647159, 970739, 1456109, 2184164, 3276246, 4914369, 7371554, 11057332
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| It is an important unsolved problem related to Waring's problem to show that a(n) = floor((3^n-1)/(2^n-1)) holds for all n >= 1. This has been checked for 10000 terms and is true for all sufficiently large n, by a theorem of Mahler. [Lichiardopol]
a(n) = floor((3^n-1)/(2^n-1)) holds true at least for 2<=n<=305000. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 31 2008
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REFERENCES
| R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), no. 1, 3-20.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 82.
N. Lichiardopol, Problem 925 (BCC20.19), A number-theoretic problem, in Research Problems from the 20th British Combinatorial Conference, Discrete Math., 308 (2008), 621-630.
K. Mahler, On the fractional parts of the powers of a rational number, II, Mathematika 4 (1957), 122-124.
S. S. Pillai, On Waring's problem, J. Indian Math. Soc., 2 (1936), 16-44.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Power Floors
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FORMULA
| a(n)=b(n)-(-2/3)^n where b(n) is defined by the recursion b(0):=2, b(1):=5/6, b(n+1):=(5/6)*b(n)+b(n-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 31 2008
a(n)=(1/2)*(b(n)+sqrt(b(n)^2-(-4)^n)) (with b(n) as defined above). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 31 2008
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MATHEMATICA
| Table[ Floor[(3/2)^n], {n, 0, 40}] (from Robert G. Wilson v)
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PROG
| (PARI) a(n)=3^n>>n \\ Charles R Greathouse IV, Jun 10 2011
(MAGMA) [Floor(3^n / 2^n): n in [0..40]]; // Vincenzo Librandi, Sep 08 2011
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CROSSREFS
| Cf. A094969-A094500, A000217, A081464, A153662, A153665, A153666.
Sequence in context: A068523 A055500 A018058 * A072465 A204631 A052284
Adjacent sequences: A002376 A002377 A002378 * A002380 A002381 A002382
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2004
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