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Search: id:A002379
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| A002379 |
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Floor [ 3^n / 2^n ].
(Formerly M0666 N0245)
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+0
59
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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; listen)
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OFFSET
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0,3
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COMMENT
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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]
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REFERENCES
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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 Britsh 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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Power Floors
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MATHEMATICA
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Table[ Floor[(3/2)^n], {n, 0, 40}] (from Robert G. Wilson v)
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CROSSREFS
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Cf. A094969 - A094500.
Sequence in context: A068523 A055500 A018058 this_sequence A072465 A052284 A133670
Adjacent sequences: A002376 A002377 A002378 this_sequence A002380 A002381 A002382
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 11 2004
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