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A060007 Decimal expansion of v_4, where v_n is the smallest, positive, real solution to the equation (v_n)^n = v_n + 1. 11
1, 2, 2, 0, 7, 4, 4, 0, 8, 4, 6, 0, 5, 7, 5, 9, 4, 7, 5, 3, 6, 1, 6, 8, 5, 3, 4, 9, 1, 0, 8, 8, 3, 1, 9, 1, 4, 4, 3, 2, 4, 8, 9, 0, 8, 6, 2, 4, 8, 6, 3, 5, 2, 1, 4, 2, 8, 8, 2, 4, 4, 4, 5, 3, 0, 4, 9, 7, 1, 0, 0, 0, 8, 5, 2, 2, 5, 9, 1, 3, 5, 0, 2, 5, 3, 0, 9, 5, 5, 2, 1, 8, 6, 9, 9, 6, 2, 8, 6, 2, 5, 7, 4, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

v_2 = A001622.

A Perron number of the 4th degree polynomial (see Boys and Wu). - R. J. Mathar, Mar 19 2011

This number is not ruler-and-compass constructible because x^4-x-1 and its resolvent x^3+4x+1 are irreducible over the rationals. - Jean-François Alcover, Aug 31 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

David W. Boys, The maximal modulus of an algebraic integer, Math. Comp. 45 (1985) 243-249, table page S18.

F. Rothelius, Formulae [broken link]

Qiang Wu, The smallest Perron numbers, Math. Comp. 79 (2010) 2387-2394

FORMULA

Equals (1 + (1 + (1 + (1 + (1 + ...)^(1/4))^(1/4))^(1/4))^(1/4))^(1/4). - Ilya Gutkovskiy, Dec 15 2017

EXAMPLE

v_4 = 1.220744084605759475361685349...

MAPLE

r:=(108+12*sqrt(849))^(1/3): (sqrt(12/sqrt(-8/r+r/6)+48/r-r) + sqrt(-48/r+r))/(2*sqrt(6)): evalf(%, 105); # Vaclav Kotesovec, Oct 12 2013

MATHEMATICA

RealDigits[x/.FindRoot[x^4==x+1, {x, 1}, WorkingPrecision->120]][[1]] (* Harvey P. Dale, Jul 11 2012 *)

Root[ #^4 - # - 1&, 2] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Mar 04 2013 *)

CROSSREFS

Cf. A001622, A060006, A160155.

Sequence in context: A243492 A086118 A104986 * A021457 A305605 A137456

Adjacent sequences:  A060004 A060005 A060006 * A060008 A060009 A060010

KEYWORD

cons,nice,nonn

AUTHOR

Fabian Rothelius, Mar 14 2001

EXTENSIONS

More terms from Benoit Cloitre, Jan 11 2003

STATUS

approved

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Last modified June 22 20:34 EDT 2021. Contains 345388 sequences. (Running on oeis4.)