A175801 Number of real zeros of the polynomial whose coefficients are the decimal digits of prime(n).

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, 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, 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

Offset: 1

Author

Michel Lagneau, Dec 04 2010

Keywords

• nonn
• base

Comments

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

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

Examples

			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...
		

Crossrefs

Cf. A173667.

Programs

Maple

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:
seq(A175801(n),n=1..45) ; # R. J. Mathar, Dec 06 2010