cp's OEIS Frontend

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

%I A175800 #15 May 12 2019 02:22:55
%S A175800 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,
%T A175800 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,
%U A175800 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
%N A175800 Number of real zeros of the polynomial whose coefficients are the decimal digits of Fibonacci(n).
%C A175800 a(n) is the number of real zeros of the polynomial Sum_{k=0..p} d(k)*x^k
%C A175800   where d(k) are the decimal digits of Fibonacci(n) = Sum_{i>=0} 10^i*d(i).
%e A175800 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...
%p A175800 A175800 := proc(n)
%p A175800         d := convert(combinat[fibonacci](n),base,10) ;
%p A175800         P := add( op(i,d)*x^(i-1),i=1..nops(d)) ;
%p A175800         [fsolve(P,x,real)] ;
%p A175800         nops(%) ;
%p A175800 end proc:
%p A175800 seq(A175800(n),n=1..45) ; # _R. J. Mathar_, Dec 06 2010
%Y A175800 Cf. A000045, A173667.
%K A175800 nonn,base
%O A175800 1,12
%A A175800 _Michel Lagneau_, Dec 04 2010