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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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1
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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
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OFFSET
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1,2
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COMMENTS
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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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FORMULA
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a(n) = 2^n*floor((3/2)^n) - 1 = 2^n*A002379(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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MAPLE
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2^n*floor((3/2)^n)-1
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MATHEMATICA
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a[n_]:=-1+2^n*Floor[(3/2)^n]
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PROG
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(Python)
def a(n): return (3**n//2**n-1)*2**n + (2**n-1)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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