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A092526 Decimal expansion of (2/3)*cos( (1/3)*arccos(29/2) ) + 1/3. 8
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

This is the limit x of the ratio N(n+1)/N(n) for n -> infinity of the Narayana sequence N(n) = A000930(n). The real root of x^3 - x^2 - 1. See the formula section. - Wolfdieter Lang, Apr 24 2015

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, Chap. 7: Some Combinational Logic Examples, Section 7.1: Channel Capacity, Shannon's Theorem, and Error-Detection Theory, page 120.

LINKS

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

H. R. P. Ferguson, On a Generalization of the Fibonacci Numbers Useful in Memory Allocation Schema or All About the Zeroes of Z^k - Z^{k - 1} - 1, k > 0 , Fibonacci Quarterly, Volume 14, Number 3, October, 1976 (see Table 2 p. 238).

FORMULA

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

The only real irrational root of x^4-x^2-x-1 (-1 is also a root). [Nahim]

Equals 1 + A088559.

Equals (1/6)*(116+12*sqrt(93))^(1/3) + 2/(3*(116+12*sqrt(93))^(1/3)) + 1/3. - Vaclav Kotesovec, Dec 18 2014

EXAMPLE

=1.46557123187676802665673122521993910802557756847228570164318311124926...

MATHEMATICA

RealDigits[(2 Cos[ ArcCos[ 29/2]/3] + 1)/3, 10, 111][[1]] (* 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

Cf. A088559, A076725, A000930.

Sequence in context: A200497 A271365 A088559 * A243396 A140243 A023825

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 June 28 21:19 EDT 2016. Contains 274271 sequences.