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 A018886 Waring's problem: least positive integer requiring maximum number of terms when expressed as a sum of positive n-th powers. 2
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 393. LINKS T. D. Noe, Table of n, a(n) for n = 1..200 P. Pollack, Analytic and Combinatorial Number Theory Course Notes, exercise 7.1.1. p. 277. Eric Weisstein's World of Mathematics, Waring's Problem. FORMULA a(n) = 2^n*floor((3/2)^n) - 1 = 2^n*A002379(n) - 1. EXAMPLE 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. MAPLE A018886 := proc(n) 2^n*floor((3/2)^n)-1 end proc: # R. J. Mathar, May 07 2015 MATHEMATICA a[n_]:=-1+2^n*Floor[(3/2)^n] a[Range[1, 20]] (* Julien Kluge, Jul 21 2016 *) PROG (Python) def a(n): return (3**n//2**n-1)*2**n + (2**n-1) print([a(n) for n in range(1, 27)]) # Michael S. Branicky, Dec 17 2021 (Python) def A018886(n): return (3**n&-(1<

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Last modified August 12 19:26 EDT 2024. Contains 375113 sequences. (Running on oeis4.)