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A174420 Let A(n) = floor((3/2)^n), B(n)=3^n-2^n*A(n); then a(n)=2^n-A(n)-B(n)-2. 1
-2, -2, -1, 0, 8, 4, 26, 98, 68, 245, 284, 941, 908, 2921, 866, 3038, 9773, 95842, 26864, 82811, 776048, 235984, 715436, 2157533, 14878043, 27882168, 16575521, 116892244, 82326503, 515542801, 1009949246, 882651721, 500902958, 1503356036, 4511038850, 13534572662, 40605902153, 53101505973, 21870478820, 65618808017 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Related to Waring's problem.

a(n) is conjectured to be >= 0 for all n >= 3. If this were proved it would settle Waring's problem (see A002804). It is known that a(n) >= 0 for 3 <= n <= 471600000.

REFERENCES

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 337.

R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, pp. 285-324 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.

LINKS

Table of n, a(n) for n=0..39.

M. Waldschmidt, Open Diophantine problems

MATHEMATICA

a[n_] := Floor[(3/2)^n]; b[n_] := 3^n - 2^n*a[n]; Table[2^n - a[n] - b[n] - 2, {n, 0, 39}] (* Jean-Fran├žois Alcover, Apr 05 2011 *)

CROSSREFS

Cf. A002804.

Sequence in context: A327365 A093729 A113080 * A266318 A011265 A265863

Adjacent sequences:  A174417 A174418 A174419 * A174421 A174422 A174423

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2010

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)