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A132338 Decimal expansion of 1 - 1/phi. 5
3, 8, 1, 9, 6, 6, 0, 1, 1, 2, 5, 0, 1, 0, 5, 1, 5, 1, 7, 9, 5, 4, 1, 3, 1, 6, 5, 6, 3, 4, 3, 6, 1, 8, 8, 2, 2, 7, 9, 6, 9, 0, 8, 2, 0, 1, 9, 4, 2, 3, 7, 1, 3, 7, 8, 6, 4, 5, 5, 1, 3, 7, 7, 2, 9, 4, 7, 3, 9, 5, 3, 7, 1, 8, 1, 0, 9, 7, 5, 5, 0, 2, 9, 2, 7, 9, 2, 7, 9, 5, 8, 1, 0, 6, 0, 8, 8, 6, 2, 5, 1, 5, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Density of 1's in Fibonacci word A003849.

Decimal expansion of 2 - phi. [Omar E. Pol, Jan 28 2009]

Also decimal expansion of sum(n>=1, ((-1)^(n+1))*1/phi^n ). [Michel Lagneau, Dec 04 2011]

The Lambert series evaluated at this point is 0.8828541617125076... [see Andre-Jeannin]. - R. J. Mathar, Oct 28 2012

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

R. Andre-Jeannin, Lambert series and the summation of reciprocals in certain Fibonacci-Lucas-Type sequences, Fib. Quart. 28 (1990) 223-226

FORMULA

Equals A094874 - 1, or A079585 - 2, or the square of A094214.

Equals (5-sqrt(5))^2/20 = 1/phi^2 = 1/A104457. [Joost Gielen, Sep 28 2013] (corrected, Joerg Arndt, Sep 29 2013)

EXAMPLE

0.38196601125010515179541316563436188...

MATHEMATICA

RealDigits[N[1/GoldenRatio^2, 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

CROSSREFS

Cf. A001622.

Sequence in context: A016622 A143623 A094874 * A132702 A197725 A022833

Adjacent sequences:  A132335 A132336 A132337 * A132339 A132340 A132341

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Nov 07 2007

STATUS

approved

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Last modified February 28 23:17 EST 2015. Contains 255098 sequences.