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%I #12 May 12 2019 02:23:00
%S 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,2,0,0,
%T 0,2,0,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,2,2,0,2,0,2,0,2,2,2,0,0,0,0,0,0,
%U 0,0,0,0,0,2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2,0,0
%N Number of real zeros of the polynomial whose coefficients are the decimal digits of prime(n).
%C a(n) is the number of real zeros of the polynomial Sum_{k>=0} d(k) x^k
%C where d(k) are the digits of the decimal expansion of prime(n) = Sum_{k>=0} 10^k*d(k).
%e a(167) = 2 because prime(167) = 991 => P(167,x) = 1 + 9*x + 9*x^2 has 2 real-valued roots, -0.8726779962... and -0.1273220038...
%p A175801 := proc(n) d := convert(ithprime(n),base,10) ; P := add( op(i,d)*x^(i-1),i=1..nops(d)) ; [fsolve(P,x,real)] ; nops(%) ; end proc:
%p seq(A175801(n),n=1..45) ; # _R. J. Mathar_, Dec 06 2010
%Y Cf. A173667.
%K nonn,base
%O 1,32
%A _Michel Lagneau_, Dec 04 2010
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