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A263719
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Decimal expansion of the real root r of r^3 + r - 1 = 0.
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10
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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
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OFFSET
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0,1
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COMMENTS
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Constant from Narayana's cows sequence: Limit A000930(n)/A000930(n+1) = r.
Reciprocal of constant described by A092526.
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LINKS
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FORMULA
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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.
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EXAMPLE
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0.682327803828019327369483739711048256891188581897998577803728606639896...
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MATHEMATICA
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RealDigits[ ((Sqrt[93] + 9)/18)^(1/3) - ((Sqrt[93] - 9)/18)^(1/3), 10, 100][[1]] (* G. C. Greubel, May 01 2017 *)
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PROG
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(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), ", "))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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