OFFSET
1,4
COMMENTS
The sequence is conjectured to contain an infinite number of primes. The first 100 terms contain 33 unique primes. As stated by Everest and Ward, except for a finite number of composite n, a(n) can be prime only if n is prime. For this sequence, n=23*47 is the largest composite for which a(n) is prime.
REFERENCES
M. Einsiedler, G. Everest, T. Ward, Primes in sequences associated to polynomials, LMS J. Comp. Math. 3 (2000), 15-29
G. Everest, T. Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer, London, 1999.
LINKS
G. Everest and T. Ward, Primes in Divisibility Sequences, Cubo Matematica Educacional (2001), 3 (2), pp. 245-259.
MATHEMATICA
CompanionMatrix[p_, x_] := Module[{cl=CoefficientList[p, x], deg, m}, cl=Drop[cl/Last[cl], -1]; deg=Length[cl]; If[deg==1, {-cl}, m=RotateLeft[IdentityMatrix[deg]]; m[[ -1]]=-cl; Transpose[m]]]; c=CompanionMatrix[x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1, x]; im=IdentityMatrix[10]; tmp=im; Table[tmp=tmp.c; Sqrt[Abs[Det[tmp-im]]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Sep 15 2003
STATUS
approved