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A086596
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An invariant of the set {Log(2), Log(3), Log(5),..., Log(Prime(2n)), Log(Prime(2n+1))}.
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1
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1, -1, 3, -8, 22, -53, 158, -481, 1471, -4621, 14612
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence comes from a corrected and extended example in the paper by Besser and Moree.
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REFERENCES
| D. Gijswijt and P. Moree, A set-theoretic invariant, (vide the ArXiv or http://staff.science.uva.nl/~moree/preprints.html)
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LINKS
| A. Besser, P. Moree, On an invariant related to a linear inequality, Arch. Math. 79: pp. 463-471
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
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FORMULA
| a(t)=(-1)^t/2 sum_{d|p_1...p_t, d\le \sqrt{p_1...p_t}mu(d),
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MATHEMATICA
| 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}]
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CROSSREFS
| Cf. A068101.
Sequence in context: A202192 A027211 A027235 * A036882 A020962 A027243
Adjacent sequences: A086593 A086594 A086595 * A086597 A086598 A086599
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KEYWORD
| hard,sign,more
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Aug 01 2003
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