Search: id:A002379
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%I A002379 M0666 N0245
%S A002379 1,1,2,3,5,7,11,17,25,38,57,86,129,194,291,437,656,985,1477,2216,3325,
%T A002379 4987,7481,11222,16834,25251,37876,56815,85222,127834,191751,287626,
%U A002379 431439,647159,970739,1456109,2184164,3276246,4914369,7371554,11057332
%N A002379 Floor [ 3^n / 2^n ].
%C A002379 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]
%C A002379 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
%D A002379 R. K. Guy, The second strong law of small numbers. Math. Mag. 63 (1990), 
               no. 1, 3-20.
%D A002379 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 
               105, National Research Council, Washington, DC, 1941, p. 82.
%D A002379 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.
%D A002379 K. Mahler, On the fractional parts of the powers of a rational number, 
               II, Mathematika 4 (1957), 122-124.
%D A002379 S. S. Pillai, On Waring's problem, J. Indian Math. Soc., 2 (1936), 16-44.
%D A002379 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002379 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002379 T. D. Noe, <a href="b002379.txt">Table of n, a(n) for n=0..1000</a>
%H A002379 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PowerFloors.html">Power Floors</a>
%F A002379 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
%F A002379 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
%t A002379 Table[ Floor[(3/2)^n], {n, 0, 40}] (from Robert G. Wilson v)
%Y A002379 Cf. A094969 - A094500.
%Y A002379 Cf. A000217, A153661, A153662, A153665, A153666.
%Y A002379 Sequence in context: A068523 A055500 A018058 this_sequence A072465 A052284 
               A133670
%Y A002379 Adjacent sequences: A002376 A002377 A002378 this_sequence A002380 A002381 
               A002382
%K A002379 nonn,easy
%O A002379 0,3
%A A002379 N. J. A. Sloane (njas(AT)research.att.com).
%E A002379 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2004

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