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A255941
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Decimal expansion of A such that y = A*x^2 cuts the triangle with vertices (0,0), (1,0), (0,1) into two equal areas.
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0
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3, 3, 1, 2, 3, 7, 6, 4, 7, 7, 8, 7, 1, 3, 2, 1, 8, 5, 1, 1, 1, 0, 4, 9, 6, 4, 1, 3, 5, 7, 3, 7, 3, 2, 5, 1, 8, 7, 3, 3, 0, 8, 6, 1, 8, 8, 5, 1, 4, 0, 0, 9, 3, 4, 8, 2, 5, 4, 1, 6, 9, 3, 6, 2, 6, 6, 2, 5, 5, 2, 4, 6, 5, 9, 1, 0, 6, 8, 7, 9, 0, 0, 7, 4, 6, 8, 0, 4, 5, 0, 4, 6, 5, 5, 1, 6, 6, 8, 3, 0, 6, 5, 9, 6, 3, 7, 3, 8, 0
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OFFSET
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1,1
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COMMENTS
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A is found by solving the equation A*x^2+3*A^2*x^3 = 3 or equivalently 3*A*x^2+(1-3*A)*x+2 = 0 where x = (-1+sqrt(1+4*A))/(2*A) in both equations. Using the quadratic formula, one can reduce this equation to solely sqrt(9*A^2-30*A+1)+3*sqrt(4*A+1) = 3*A+2.
Also, decimal expansion of (14+5*sqrt(10))/9.
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LINKS
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Table of n, a(n) for n=1..109.
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FORMULA
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( 14 + 5*sqrt(10) )/9.
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EXAMPLE
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3.31237647787132185111049641357373251873308...
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PROG
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(PARI) default(realprecision, 110); x=(14+5*sqrt(10))/9; for(n=1, 100, d=floor(x); x=(x-d)*10; print1(d, ", "))
(PARI) (14+5*sqrt(10))/9
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CROSSREFS
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Sequence in context: A004550 A096836 A096995 * A010264 A262816 A089680
Adjacent sequences: A255938 A255939 A255940 * A255942 A255943 A255944
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Derek Orr, Mar 11 2015
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STATUS
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approved
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