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A092526 Decimal expansion of (2/3)*cos( (1/3)*arccos(29/2) ) + 1/3. 7
1, 4, 6, 5, 5, 7, 1, 2, 3, 1, 8, 7, 6, 7, 6, 8, 0, 2, 6, 6, 5, 6, 7, 3, 1, 2, 2, 5, 2, 1, 9, 9, 3, 9, 1, 0, 8, 0, 2, 5, 5, 7, 7, 5, 6, 8, 4, 7, 2, 2, 8, 5, 7, 0, 1, 6, 4, 3, 1, 8, 3, 1, 1, 1, 2, 4, 9, 2, 6, 2, 9, 9, 6, 6, 8, 5, 0, 1, 7, 8, 4, 0, 4, 7, 8, 1, 2, 5, 8, 0, 1, 1, 9, 4, 9, 0, 9, 2, 7, 0, 0, 6, 4, 3, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The only non-imaginary irrational root of x^4-x^2-x-1==0. -1 is also a root. (Nahim).

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.3.

Paul J. Nahin, The Logician and the Engineer, How George Boole and Claude Shannon Created the Information Age, Princeton University Press, Princeton and Oxford, 2013, Chpt. 7 Some Combinational Logic Examples, 7.1 Channel Capacity, Shannon's Theorem, and Error-Detection Theory, pg 120.

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,20000

FORMULA

Real root of x^3 - x^2 - 1. - Franklin T. Adams-Watters, Oct 12 2006

1.46557123187676... = 1 + A088559 constant.

EXAMPLE

=1.46557123187676802665673122521993910802557756847228570164318311124926...

MATHEMATICA

RealDigits[(2 Cos[ ArcCos[ 29/2]/3] + 1)/3, 10, 111][[1]] (from Robert G. Wilson v Apr 12 2004)

RealDigits[ Solve[ x^3 - x^2 - 1 == 0, x][[1, 1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Oct 10 2013 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 20080); x=solve(x=1, 2, x^3 - x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b092526.txt", n, " ", d)); } [Harry J. Smith, Jun 21 2009]

CROSSREFS

Sequence in context: A062117 A200497 A088559 * A140243 A023825 A199289

Adjacent sequences:  A092523 A092524 A092525 * A092527 A092528 A092529

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane, Apr 07 2004

EXTENSIONS

More terms from Robert G. Wilson v, Apr 12 2004

STATUS

approved

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Last modified April 16 03:40 EDT 2014. Contains 240534 sequences.