A014011 Defined by a chi-inequality greedy algorithm.

1, 2, 4, 6, 9, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 120, 126, 133, 140, 147, 154, 161, 168, 176, 184, 192, 200, 208, 216, 225, 234, 243, 252, 261, 270, 280, 290, 300, 310, 320, 330, 341, 352, 363, 374, 385

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 163-166.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Yong-Gao Chen, On the reciprocal sum of a sum-free sequence, Sci China Math, 2013, 56: 951-966, doi:10.1007/s11425-012-4540-6.

Steven R. Finch, A Convex Maximization Problem [Broken link]

Steven R. Finch, A convex maximization problem: Discrete case, arXiv:math/9912035 [math.OC], 1999, and Continuous Case.

Steven R. Finch, Erdos's Reciprocal Sum Constants [Broken link]

Steven R. Finch, Erdos's Reciprocal Sum Constants [From the Wayback machine]

E. Levine and J. O'Sullivan, An upper estimate for the reciprocal sum of a sum-free sequence, Acta Arithmetica, 34 (1977), 9-24.

Eric Weisstein's World of Mathematics, Levine-O'Sullivan Sequence.

Formula

a(n) = max{(k+1)*(n-a(k)): 1<=k<n}, a(1) = 1. - Reinhard Zumkeller, Jul 10 2013

Mathematica

a[1] = 1; a[n_] := a[n] = Table[(k+1)*(n-a[k]), {k, 1, n-1}] // Max; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, May 07 2014 *)

Prog

(Haskell)
a014011 n = a014011_list !! (n-1)
a014011_list = 1 : f 2 [1] where
   f u vs = w : f (u + 1) (w : vs) where
     w = maximum $ zipWith (*) [u, u-1 ..] $ map (u -) vs
-- Reinhard Zumkeller, Jul 10 2013
(PARI)
seq(N) = {
  my(a = vector(N)); a[1] = 1;
  for (n = 2, N, for (k = 1, n-1, a[n] = max(a[n], (k+1)*(n-a[k]))));
  return(a);
};
seq(59)  \\ Gheorghe Coserea, Jun 12 2016

Crossrefs

Cf. A051741, A051742.

Cf. A226390 (first differences).

Sequence in context: A352191 A256393 A130664 * A064424 A067850 A130240

Adjacent sequences: A014008 A014009 A014010 * A014012 A014013 A014014

Keyword

nonn,nice

Author

Simon Plouffe

Extensions

More terms from Steven Finch, Dec 07 1999

Status

approved