A255941 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.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..109.

Formula

( 14 + 5*sqrt(10) )/9.

Example

3.31237647787132185111049641357373251873308...

Prog

(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

Crossrefs

Sequence in context: A096836 A360530 A096995 * A010264 A262816 A089680

Adjacent sequences: A255938 A255939 A255940 * A255942 A255943 A255944

Keyword

nonn,cons,easy

Author

Derek Orr, Mar 11 2015

Status

approved