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

1,32

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).

Links

Table of n, a(n) for n=1..107.

Example

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...

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

Crossrefs

Cf. A173667.

Sequence in context: A079169 A345060 A097106 * A361250 A165619 A368118

Adjacent sequences: A175798 A175799 A175800 * A175802 A175803 A175804

Keyword

nonn,base

Author

Michel Lagneau, Dec 04 2010

Status

approved