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

1,3

Comments

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

Links

Table of n, a(n) for n=1..11.

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)

Formula

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

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}]

Crossrefs

Cf. A068101.

Sequence in context: A202192 A027211 A027235 * A036882 A020962 A027243

Adjacent sequences: A086593 A086594 A086595 * A086597 A086598 A086599

Keyword

hard,sign,more

Author

T. D. Noe, Aug 01 2003

Status

approved