A116425 - OEIS

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A116425

Decimal expansion of 2 + 2*cos(2*Pi/7).

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

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OFFSET

1,1

COMMENTS

A root of the equation x^3 - 5*x^2 + 6*x - 1 = 0. - Arkadiusz Wesolowski, Jan 13 2016

The other two roots of this minimal polynomial of the present algebraic number (rho(7))^2, with rho(7) = 2*cos(Pi/7) = A160389 are (2*cos(3*Pi/7))^2 = (A255241)^2 and (2*cos(5*Pi/7))^2 = (-A255249)^2. - Wolfdieter Lang, Mar 30 2020

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.25 Tutte-Beraha Constants, p. 417.

LINKS

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

Jesús Salas and Alan D. Sokal, Transfer matrices and partition functions zeros for antiferromagnetic Potts models, arXiv:cond-mat/0004330 [cond-mat.stat-mech], 2000-2001, p. 64.

Eric Weisstein's World of Mathematics, Logistic Map

Eric Weisstein's World of Mathematics, Silver Constant

Index entries for algebraic numbers, degree 3

FORMULA

Equals (2*cos(Pi/7))^2 = (A160389)^2.

Equals 2 + i^(4/7) - i^(10/7). - Peter Luschny, Apr 04 2020

Let c = 2 + 2*cos(2*Pi/7). The linear fractional transformation z -> c - c/z has order 7, that is, z = c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/z)))))). - Peter Bala, May 09 2024

EXAMPLE

3.246979603717467061...

MATHEMATICA

First@ RealDigits[N[2 + 2 Cos[2 Pi/7], 120]] (* Michael De Vlieger, Jan 13 2016 *)

PROG

(PARI) 2 + 2*cos(2*Pi/7) \\ Michel Marcus, Jan 13 2016

CROSSREFS

Cf. A231187, A160389.

Cf. A003558, A054142, A255241, A255249.

2 + 2*cos(2*Pi/n): A104457 (n = 5), A332438 (n = 9), A296184 (n = 10), A019973 (n = 12).

Sequence in context: A138245 A163328 A164109 * A019653 A240493 A095258

Adjacent sequences: A116422 A116423 A116424 * A116426 A116427 A116428

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Feb 15 2006

STATUS

approved