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A055060 Decimal expansion of Komornik-Loreti constant. 3
1, 7, 8, 7, 2, 3, 1, 6, 5, 0, 1, 8, 2, 9, 6, 5, 9, 3, 3, 0, 1, 3, 2, 7, 4, 8, 9, 0, 3, 3, 7, 0, 0, 8, 3, 8, 5, 3, 3, 7, 9, 3, 1, 4, 0, 2, 9, 6, 1, 8, 1, 0, 9, 9, 7, 7, 8, 4, 7, 8, 1, 4, 7, 0, 5, 0, 5, 5, 5, 7, 4, 9, 1, 7, 5, 0, 6, 0, 5, 6, 8, 6, 9, 9, 1, 3, 1, 0, 0, 1, 8, 6, 3, 4, 0, 7, 5, 3, 3, 3, 0, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..102.

J.-P. Allouche and M. Cosnard, The Komornik-Loreti constant is transcendental

J.-P. Allouche and M. Cosnard, The Komornik-Loreti constant is transcendental, Amer. Math. Monthly, 107 (No. 5, May, 2000), 448-449.

Vilmos Komornik and Paola Loreti, Unique Developments in Non-Integer Bases, Amer. Math. Monthly, Vol. 105, No. 7 (Aug. - Sep., 1998), pp. 636-639.

Vilmos Komornik, Derong Kong, Bases with two expansions, arXiv:1705.00473 [math.NT], 2017.

Eric Weisstein's World of Mathematics, Komornik-Loreti Constant

FORMULA

This number q (say) is defined by 1 = Sum_{n >= 1} A010060(n)/q^n.

EXAMPLE

1.787231650...

MATHEMATICA

First[ RealDigits[q /. FindRoot[ Sum[ Mod[ DigitCount[n, 2, 1], 2]/q^n, {n, 1, 2000}] == 1, {q, 1.8}, WorkingPrecision -> 120], 10, 102]](* Jean-Fran├žois Alcover, Jun 11 2012, after PARI *)

PROG

(PARI) solve(q=1.7, 1.8, sum(n=1, 2000, (subst(Pol(binary(n)), x, 1)%2)/q^n)-1)

CROSSREFS

The continued-fraction expansion of this number is in A080890.

Sequence in context: A020506 A193345 A197822 * A010515 A021131 A220610

Adjacent sequences:  A055057 A055058 A055059 * A055061 A055062 A055063

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane, Jun 11 2000

EXTENSIONS

More terms from Ralf Stephan, Mar 30 2003

STATUS

approved

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Last modified July 24 18:02 EDT 2017. Contains 289776 sequences.