MathDB

Suppose a real number

a

is a root of a polynomial with integer coefficients

P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0

. Let

G=|a_n|+|a_{n-1}|+...+|a_1|+|a_0|

. We say that

G

is a gingado of

a

. For example, as

2

is root of

P(x)=x^2-x-2

G=|1|+|-1|+|-2|=4

, we say that

4

is a gingado of

2

. What is the fourth largest real number

a

such that

3

is a gingado of

a

3