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A086596 An invariant of the set {Log(2), Log(3), Log(5),..., Log(Prime(2n)), Log(Prime(2n+1))}. 2


%S 1,-1,3,-8,22,-53,158,-481,1471,-4621,14612

%N An invariant of the set {Log(2), Log(3), Log(5),..., Log(Prime(2n)), Log(Prime(2n+1))}.

%C This sequence comes from a corrected and extended example in the paper by Besser and Moree.

%H A. Besser, P. Moree, <a href="http://www.birkhauser.ch/journals/1300/papers/2079006/20790463.pdf">On an invariant related to a linear inequality</a>, Arch. Math. 79: pp. 463-471

%H D. Gijswijt and P. Moree, <a href="http://arxiv.org/abs/math/0309318">A set-theoretic invariant</a>, arXiv:math/0309318 (2003)

%F a(t)=(-1)^t/2 sum_{d|p_1...p_t, d <= sqrt{p_1...p_t} mu(d).

%t Invariant[a_List] := Module[{i=1, j=2, xMin, xMax, aa, n, invar=0, signs, x}, xMin=Abs[a[[i]]-a[[j]]]; xMax=a[[i]]+a[[j]]; aa=Complement[a, {a[[i]], a[[j]]}]; n=Length[aa]; Do[signs=(2*IntegerDigits[k, 2, n]-1); x=aa.signs; If[x>xMin&&x<xMax, invar+=Times@@signs], {k, 0, 2^n-1}]; invar]; Table[theSet=Table[N[Log[Prime[i]]], {i, 1, n}]; Invariant[theSet], {n, 3, 23, 2}]

%Y Cf. A068101.

%K hard,sign,more

%O 1,3

%A _T. D. Noe_, Aug 01 2003

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)