|
%I #36 Apr 18 2019 17:56:02
%S 1,2,4,6,9,12,15,18,21,24,28,32,36,40,45,50,55,60,65,70,75,80,85,90,
%T 96,102,108,114,120,126,133,140,147,154,161,168,176,184,192,200,208,
%U 216,225,234,243,252,261,270,280,290,300,310,320,330,341,352,363,374,385
%N Defined by a chi-inequality greedy algorithm.
%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 163-166.
%H Reinhard Zumkeller, <a href="/A014011/b014011.txt">Table of n, a(n) for n = 1..10000</a>
%H Yong-Gao Chen, <a href="http://dx.doi.org/10.1007/s11425-012-4540-6">On the reciprocal sum of a sum-free sequence</a>, Sci China Math, 2013, 56: 951-966, doi:10.1007/s11425-012-4540-6.
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/erdos/convex/convex.html">A Convex Maximization Problem</a> [Broken link]
%H Steven R. Finch, <a href="https://arxiv.org/abs/math/9912035">A convex maximization problem: Discrete case</a>, arXiv:math/9912035 [math.OC], 1999, and <a href="https://arxiv.org/abs/math/9912036">Continuous Case</a>.
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/erdos/erdos.html">Erdos's Reciprocal Sum Constants</a> [Broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010620000306/http://www.mathsoft.com/asolve/constant/erdos/erdos.html">Erdos's Reciprocal Sum Constants</a> [From the Wayback machine]
%H E. Levine and J. O'Sullivan, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa34/aa3412.pdf">An upper estimate for the reciprocal sum of a sum-free sequence</a>, Acta Arithmetica, 34 (1977), 9-24.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Levine-OSullivanSequence.html">Levine-O'Sullivan Sequence.</a>
%F a(n) = max{(k+1)*(n-a(k)): 1<=k<n}, a(1) = 1. - _Reinhard Zumkeller_, Jul 10 2013
%t 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 *)
%o (Haskell)
%o a014011 n = a014011_list !! (n-1)
%o a014011_list = 1 : f 2 [1] where
%o f u vs = w : f (u + 1) (w : vs) where
%o w = maximum $ zipWith (*) [u, u-1 ..] $ map (u -) vs
%o -- _Reinhard Zumkeller_, Jul 10 2013
%o (PARI)
%o seq(N) = {
%o my(a = vector(N)); a[1] = 1;
%o for (n = 2, N, for (k = 1, n-1, a[n] = max(a[n], (k+1)*(n-a[k]))));
%o return(a);
%o };
%o seq(59) \\ _Gheorghe Coserea_, Jun 12 2016
%Y Cf. A051741, A051742.
%Y Cf. A226390 (first differences).
%K nonn,nice
%O 1,2
%A _Simon Plouffe_
%E More terms from _Steven Finch_, Dec 07 1999
|
