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A014011 Defined by a chi-inequality greedy algorithm. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A143145 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

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)