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A263719 Decimal expansion of the real root r of r^3 + r - 1 = 0. 8
6, 8, 2, 3, 2, 7, 8, 0, 3, 8, 2, 8, 0, 1, 9, 3, 2, 7, 3, 6, 9, 4, 8, 3, 7, 3, 9, 7, 1, 1, 0, 4, 8, 2, 5, 6, 8, 9, 1, 1, 8, 8, 5, 8, 1, 8, 9, 7, 9, 9, 8, 5, 7, 7, 8, 0, 3, 7, 2, 8, 6, 0, 6, 6, 3, 9, 8, 9, 6, 6, 7, 8, 6, 8, 6, 9, 9, 8, 0, 2, 1, 0, 8, 1, 7, 3, 2, 0, 4, 3, 7, 8, 6, 2, 0, 5, 1, 2, 8, 2, 9, 5, 5, 9, 3, 3, 1, 8, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Constant from Narayana's cows sequence: Limit A000930(n)/A000930(n+1) = r.

Reciprocal of constant described by A092526.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

FORMULA

r = (sqrt(93)/18 + 1/2)^(1/3) - (sqrt(93)/18 - 1/2)^(1/3).

Constant r satisfies:

(1) 1/(1 - r*I) = (r + r^2*I) where I^2 = -1.

(2) r = real( 1/(1 - r*I) ).

(3) r = norm( 1/(1 - r*I) ).

(4) r = r^2 + r^4.

Equals 1/A092526. - Vaclav Kotesovec, Nov 27 2017

EXAMPLE

0.682327803828019327369483739711048256891188581897998577803728606639896...

MATHEMATICA

RealDigits[ ((Sqrt[93] + 9)/18)^(1/3) - ((Sqrt[93] - 9)/18)^(1/3), 10, 100][[1]] (* G. C. Greubel, May 01 2017 *)

PROG

(PARI) {a(n) = my(r = (sqrt(93)/18 + 1/2)^(1/3) - (sqrt(93)/18 - 1/2)^(1/3)); floor(r*10^(n+1))%10}

for(n=0, 120, print1(a(n), ", "))

(PARI) solve(r=0, 1,  r^3 + r - 1 ) \\ Michel Marcus, Oct 25 2015

CROSSREFS

Cf. A000930, A025157, A076725, A092526, A274112.

Sequence in context: A196617 A021860 A161015 * A154564 A152914 A178647

Adjacent sequences:  A263716 A263717 A263718 * A263720 A263721 A263722

KEYWORD

nonn,cons

AUTHOR

Paul D. Hanna, Oct 24 2015

STATUS

approved

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Last modified December 6 18:16 EST 2021. Contains 349567 sequences. (Running on oeis4.)