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A002804 (Presumed) solution to Waring's problem: g(n) = 2^n + [ 1.5^n ] - 2.
(Formerly M3361 N1353)
+0
5
1, 4, 9, 19, 37, 73, 143, 279, 548, 1079, 2132, 4223, 8384, 16673, 33203, 66190, 132055, 263619, 526502, 1051899, 2102137, 4201783, 8399828, 16794048, 33579681, 67146738, 134274541, 268520676, 536998744, 1073933573, 2147771272 (list; graph; listen)
OFFSET

1,2

REFERENCES

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).

L. E. Dickson, The Waring Problem and its generalizations, Bulletin of the AMS, 42 (1936) 833-842.

G. H. Hardy, Collected Papers. Vols. 1-, Oxford Univ. Press, 1966-; see vol. 1, p. 668.

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

K. Mahler, On the fractional parts of the powers of a rational number (II), Mathematika, 4 (1957) 122-124 Math. Rev. 20:33.

S. Pillai, On Waring's Problem, Journal of Indian Math. Soc., 2 (1936), 16-44

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 138.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 239.

LINKS

T. D. Noe, Table of n, a(n) for n=1..200

A. V. Kumchev and D. I. Tolev, An invitation to additive number theory

M. Waldschmidt, Open Diophantine problems

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

MAPLE

A002804 := n->2^n+floor( (3/2)^n ) -2;

CROSSREFS

Sequence in context: A008113 A008111 A023611 this_sequence A133649 A101353 A008135

Adjacent sequences: A002801 A002802 A002803 this_sequence A002805 A002806 A002807

KEYWORD

nonn

AUTHOR

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

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.


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