Search: id:A086596
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%I A086596
%S A086596 1,1,3,8,22,53,158,481,1471,4621,14612
%V A086596 1,-1,3,-8,22,-53,158,-481,1471,-4621,14612
%N A086596 An invariant of the set {Log(2), Log(3), Log(5),..., Log(Prime(2n)), 
               Log(Prime(2n+1))}.
%C A086596 This sequence comes from a corrected and extended example in the paper 
               by Besser and Moree.
%D A086596 D. Gijswijt and P. Moree, A set-theoretic invariant, (vide the ArXiv 
               or http://staff.science.uva.nl/~moree/preprints.html)
%H A086596 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and 
               A. R. Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. 
               Integer Sequences, Vol. 10 (2007), #07.1.2.
%H A086596 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
%F A086596 a(t)=(-1)^t/2 sum_{d|p_1...p_t, d\le \sqrt{p_1...p_t}mu(d),
%t A086596 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 A086596 Cf. A068101.
%Y A086596 Sequence in context: A063937 A027211 A027235 this_sequence A036882 A020962 
               A027243
%Y A086596 Adjacent sequences: A086593 A086594 A086595 this_sequence A086597 A086598 
               A086599
%K A086596 hard,sign
%O A086596 1,3
%A A086596 T. D. Noe (noe(AT)sspectra.com), Aug 01 2003

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