A175800 Number of real zeros of the polynomial whose coefficients are the decimal digits of Fibonacci(n).

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 2, 0, 1, 1, 1, 1, 0, 2, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 1, 3, 1, 1, 2, 2, 0, 0, 2, 1, 1, 3, 1, 1, 4, 2, 2, 2, 1, 1, 3, 1, 1, 0, 2, 0, 2, 2, 3, 1, 1, 1, 1, 2, 2, 0, 2, 2, 1, 1, 1, 1, 2, 2, 4, 0, 0, 1, 1, 1

Offset

1,12

Comments

a(n) is the number of real zeros of the polynomial Sum_{k=0..p} d(k)*x^k

where d(k) are the decimal digits of Fibonacci(n) = Sum_{i>=0} 10^i*d(i).

Links

Table of n, a(n) for n=1..95.

Example

a(41) = 4 because Fibonacci(41) = 165580141 and the polynomial 1 + 4*x + x^2 + 8*x^4 + 5*x^5 + 5*x^6 + 6*x^7 + x^8 has 4 real roots, x0 = -5.160582776..., x2 = -1.173079878..., x3 = -0.7235395314..., and x4 = -0.2802116772...

Maple

A175800 := proc(n)
        d := convert(combinat[fibonacci](n), base, 10) ;
        P := add( op(i, d)*x^(i-1), i=1..nops(d)) ;
        [fsolve(P, x, real)] ;
        nops(%) ;
end proc:
seq(A175800(n), n=1..45) ; # R. J. Mathar, Dec 06 2010

Crossrefs

Cf. A000045, A173667.

Sequence in context: A305714 A324730 A118683 * A344981 A161116 A262726

Adjacent sequences: A175797 A175798 A175799 * A175801 A175802 A175803

Keyword

nonn,base

Author

Michel Lagneau, Dec 04 2010

Status

approved