A392802 Decimal expansion of the Mahler measure of polynomial x^6+x^5+x^4-x^3-x^2+x-1.

2, 4, 9, 6, 6, 9, 8, 2, 0, 5, 1, 6, 2, 6, 2, 2, 0, 3, 4, 0, 6, 3, 3, 1, 3, 9, 9, 1, 5, 5, 8, 3, 6, 1, 0, 2, 4, 9, 5, 7, 7, 8, 4, 0, 7, 7, 8, 0, 6, 8, 3, 9, 0, 4, 4, 7, 4, 8, 7, 3, 9, 7, 7, 9, 6, 1, 2, 8, 1, 5, 9, 0, 9, 4, 6, 9, 2, 4, 5, 9, 7, 7, 4, 8, 6, 2, 4, 8, 0, 2, 0, 1, 3, 7, 8, 6, 0, 7, 8, 2, 6, 3, 0, 8, 7

Offset

1,1

Comments

Among all sextic polynomials of the form x^6+c5*x^5+c4*x^4+c3*x^3+c2*x^2+c1*x+c0, where coefficients {c1,c2,c3,c4,c5} are {-1,0,1} and c0 are {-1,1} the biggest Mahler measure have polynomials x^6+x^5+x^4-x^3-x^2+x-1 and x^6-x^5+x^4-x^3-x^2-x-1.

Links

Table of n, a(n) for n=1..105.

Musbahu Idris and Jean-Marc Sac-Épée, Algorithmic aspects of Newman polynomials and their divisors, arXiv:2601.11486 [math.NT], 2026.

Wikipedia, Mahler measure.

Index entries for algebraic numbers, degree 4

Formula

Equals the larger of the real roots of the quartic polynomial 1-x-x^2-2*x^3+x^4.

Example

2.496698205162622034063313991558361...

Mathematica

pol = x^6 + x^5 + x^4 - x^3 - x^2 + x - 1; vec = NSolve[pol == 0, x, WorkingPrecision -> 110]; prod = 1; Do[max = Max[1, Abs[x /. vec[[n]]]]; prod = prod max, {n, 1, Length[vec]}]; RealDigits[prod, 10, 105][[1]]

Prog

(PARI) polrootsreal(x^4 - 2*x^3 - x^2 - x + 1)[2] \\ Charles R Greathouse IV, Apr 05 2026

Crossrefs

Cf. A390906, A392808.

Sequence in context: A104654 A381494 A011182 * A304753 A063507 A241473

Adjacent sequences: A392799 A392800 A392801 * A392803 A392804 A392805

Keyword

nonn,cons

Author

Artur Jasinski, Jan 23 2026

Status

approved