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A175800
Number of real zeros of the polynomial whose coefficients are the decimal digits of Fibonacci(n).
1
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).
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
Sequence in context: A305714 A324730 A118683 * A344981 A161116 A262726
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Dec 04 2010
STATUS
approved