A002376 Least number of positive cubes needed to sum to n.
1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 1, 2, 3, 4, 5, 4, 5, 6, 2, 3, 4, 5, 6, 5, 6, 7, 3, 4, 5, 6, 7, 6, 7, 8, 4, 5, 6, 2, 3, 4, 5, 6, 5, 6, 7, 3, 4, 1, 2, 3, 4, 5, 6, 4, 5, 2, 3, 4, 5, 6, 7, 5, 6, 3, 3, 4, 5, 6, 7, 6, 7, 4, 4, 5, 2, 3, 4, 5, 6, 5, 5, 6, 3, 4, 5, 6, 7, 6, 6
Offset: 1
References
- D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 81.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- A. R. Zornow, De compositione numerorum e cubis integris positivus, J. Reine Angew. Math., 14 (1835), 276-280.
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
- Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
- Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
- Eric Weisstein's World of Mathematics, Cubic Number
Crossrefs
Cf. A000578, A003325 (numbers requiring 2 cubes), A047702 (numbers requiring 3 cubes), A047703 (numbers requiring 4 cubes), A047704 (numbers requiring 5 cubes), A046040 (numbers requiring 6 cubes), A018890 (numbers requiring 7 cubes), A018888 (numbers requiring 8 or 9 cubes), A055401 (cubes needed by greedy algorithm).
Programs
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Maple
f:= proc(n) option remember; min(seq(procname(n - i^3)+1, i=1..floor(n^(1/3)))) end proc: f(0):= 0: map(f, [$1..100]); # Robert Israel, Jun 30 2017
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Mathematica
CubesCnt[n_] := Module[{k = 1}, While[Length[PowersRepresentations[n, k, 3]] == 0, k++]; k]; Array[CubesCnt, 100] (* T. D. Noe, Apr 01 2011 *) -
Python
from itertools import count from sympy.solvers.diophantine.diophantine import power_representation def A002376(n): if n == 1: return 1 for k in count(1): try: next(power_representation(n,3,k)) except: continue return k # Chai Wah Wu, Jun 25 2024
Formula
The g.f. conjectured by Simon Plouffe in his 1992 dissertation,
-(-1-z-z^2-z^3-z^4-z^5-z^6+6*z^7)/(z+1)/(z^2+1)/(z^4+1)/(z-1)^2, is incorrect: the first wrong coefficient is that of z^26. - Robert Israel, Jun 30 2017
Extensions
More terms from Arlin Anderson (starship1(AT)gmail.com)
Comments