Search: id:A018886
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%I A018886
%S A018886 1,7,23,79,223,703,2175,6399,19455,58367,176127,528383,1589247,4767743,
%T A018886 14319615,42991615,129105919,387186687,1161822207,3486515199,10458497023,
%U A018886 31377588223,94136958975,282427654143,847282962431,2541815332863
%N A018886 Waring's problem: least positive integer requiring maximum number of 
               terms when expressed as a sum of positive n-th powers.
%C A018886 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)
%D A018886 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 393
%H A018886 T. D. Noe, <a href="b018886.txt">Table of n, a(n) for n=1..200</a>
%H A018886 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WaringsProblem.html">Link to a section of The World of Mathematics.</
               a>
%H A018886 P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">
               Analytic and Combinatorial Number Theory</a> Course Notes, ex. 7.1.1.
%F A018886 a(n) = 2^n*[(3/2)^n] - 1.
%e A018886 a(3)= 23= 16+ 7= 2*(2^3) + 7*(1^3) is a sum of 9 cubes
%e A018886 a(4)= 79= 64+15= 4*(2^4) +15*(1^4) is a sum of 19 biquadrates
%Y A018886 Cf. A018887.
%Y A018886 Sequence in context: A002223 A034563 A048539 this_sequence A145842 A086908 
               A093069
%Y A018886 Adjacent sequences: A018883 A018884 A018885 this_sequence A018887 A018888 
               A018889
%K A018886 nonn,easy,nice
%O A018886 1,2
%A A018886 N. J. A. Sloane (njas(AT)research.att.com).

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