A382627 Decimal expansion of the smallest (in absolute value) root of 1-x-x^2-x^3-x^4-x^5.

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

Offset

0,1

Comments

The base of the asymptotic growth derived from Binet's formula for 5-nacci sequences.

The 5 roots are -1.0118..+-0.68395..i, 0.2575066..+-1.118790..i and this.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for algebraic numbers, degree 5

Formula

Equals 1/A103814.

Equals Sum_{k>=0} binomial(6*k+1, k)*2^(-6*k-1)/(6*k+1) = (1/2)*hypergeom([1/6, 1/3, 1/2, 2/3, 5/6], [2/5, 3/5, 4/5, 6/5], 3^6/5^5). - Stefano Spezia, Dec 23 2025

Example

0.5086603916420041364638429658984...

Mathematica

First[RealDigits[Root[#^5 + #^4 + #^3 + #^2 + # - 1 &, 1], 10, 100]] (* Paolo Xausa, Nov 24 2025 *)

Crossrefs

Cf. A103814, A001622 (Fibonacci), A192918 (3-nacci), A382626 (4-nacci).

Sequence in context: A011441 A372391 A294518 * A199729 A394966 A240358

Adjacent sequences: A382624 A382625 A382626 * A382628 A382629 A382630

Keyword

nonn,cons

Author

R. J. Mathar, Apr 01 2025

Status

approved