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A079585 Decimal expansion of c = (7-sqrt(5))/2 = 2.3819660112501... 7
2, 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

1,1

COMMENTS

c is an integer in the quadratic number field Q(sqrt(5)). - Wolfdieter Lang, Jan 08 2018

REFERENCES

J.-P. Allouche & J. Shallit, Automatic sequences, Cambridge University Press, 2003, p 65

Alfred S. Posamentier & Ingmar Lehmann, [Phi], The Glorious Golden Ratio, Prometheus Books, 2011, page 75.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10001

I. J. Good, A Reciprocal Series of Fibonacci Numbers, Fib. Quart., 12 (1974), 346.

Stanley Rabinowitz, A note on the sum 1/w_{k2^n}, Missouri J. Math. Sci. vol. 10, no. 3 (1998) pp 141-146.

Eric Weisstein's World of Mathematics, Millin Series. [Rick L. Shepherd, Aug 13 2009]

FORMULA

c = (7-sqrt(5))/2 = 4 - phi, with phi from A001622.

c = 7/2 - 10*A020837.

c = sum(k>=0, 1/F(2^k) ) where F(k) denotes the k-th Fibonacci number; c=sum(k>=0, 1/A058635(k)).

Periodic continued fraction representation is [2, 2, 1, 1, 1, 1, ....]. - R. J. Mathar, Mar 24 2011

EXAMPLE

c = 2.3819660112501051517954131656343618822796908201942371378645513772947...

MATHEMATICA

RealDigits[4 - GoldenRatio, 10, 111][[1]] (* Robert G. Wilson v, Jan 31 2012 *)

PROG

(PARI) (7 - sqrt(5))/2 \\ Michel Marcus, Sep 05 2017

CROSSREFS

Cf. A001622, A020837, A058635.

Sequence in context: A202688 A021046 A138180 * A252651 A058485 A204907

Adjacent sequences:  A079582 A079583 A079584 * A079586 A079587 A079588

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Jan 26 2003

STATUS

approved

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Last modified November 18 13:22 EST 2018. Contains 317306 sequences. (Running on oeis4.)