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Search: id:A018886
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| A018886 |
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Waring's problem: least positive integer requiring maximum number of terms when expressed as a sum of positive n-th powers. |
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+0
2
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| 1, 7, 23, 79, 223, 703, 2175, 6399, 19455, 58367, 176127, 528383, 1589247, 4767743, 14319615, 42991615, 129105919, 387186687, 1161822207, 3486515199, 10458497023, 31377588223, 94136958975, 282427654143, 847282962431, 2541815332863
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)= (Q-1)*(2^n) +(2^n-1)*(1^n) is a sum of Q +2^n -2 terms, Q= trunc(3^n / 2^n)
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 393
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, ex. 7.1.1.
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FORMULA
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a(n) = 2^n*[(3/2)^n] - 1.
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EXAMPLE
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a(3)= 23= 16+ 7= 2*(2^3) + 7*(1^3) is a sum of 9 cubes
a(4)= 79= 64+15= 4*(2^4) +15*(1^4) is a sum of 19 biquadrates
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CROSSREFS
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Cf. A018887.
Adjacent sequences: A018883 A018884 A018885 this_sequence A018887 A018888 A018889
Sequence in context: A002223 A034563 A048539 this_sequence A145842 A086908 A093069
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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