A396260 Decimal expansion of the largest root to 8*x^3 - 42*x - 7 = 0.

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

Offset

1,1

Comments

Real part of the Gauss sum tau(chi^2) = Sum_{a=0..6} chi(a)^2*exp(2*Pi*i/7), where chi is the Dirichlet character modulo 7 such that chi(3) = exp(2*Pi*i/6). Note that tau(chi^2) is a root to x^6 - 7*x^3 + 343 = 0.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 3.

Example

2.37046940557620059157...

Mathematica

First[RealDigits[Root[8*#^3 - 42*# - 7 &, 3], 10, 100]] (* Paolo Xausa, May 21 2026 *)

Prog

(PARI) solve(x=2.3, 2.4, 8*x^3 - 42*x - 7)

Crossrefs

See A396258 for table of Gauss sums of nontrivial Dirichlet characters modulo 7.

Sequence in context: A117024 A263501 A203143 * A249523 A301316 A023048

Adjacent sequences: A396256 A396258 A396259 * A396261 A396262 A396263

Keyword

nonn,cons,easy

Author

Jianing Song, May 20 2026

Status

approved