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

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

Offset: 1

Author

T. D. Noe, Aug 01 2003

Keywords

• hard
• sign
• more

Comments

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

Links

• A. Besser, P. Moree, On an invariant related to a linear inequality, Arch. Math. 79: pp. 463-471
• D. Gijswijt and P. Moree, A set-theoretic invariant, arXiv:math/0309318 (2003)

Crossrefs

Cf. A068101.

Programs

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
				

Formula

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