0,3

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

S. S. Pillai, On Waring's problem, J. Indian Math. Soc., 2 (1936), 16-44.

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.

T. D. Noe, Table of n, a(n) for n=0..1000

Eric Weisstein's World of Mathematics, Power Floors

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

Table[ Floor[(3/2)^n], {n, 0, 40}] (from Robert G. Wilson v)

Cf. A094969 - A094500.

Cf. A000217, A153661, A153662, A153665, A153666.

Adjacent sequences: A002376 A002377 A002378 this_sequence A002380 A002381 A002382

Sequence in context: A068523 A055500 A018058 this_sequence A072465 A052284 A133670

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2004