login
A175801
Number of real zeros of the polynomial whose coefficients are the decimal digits of prime(n).
1
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).
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
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Dec 04 2010
STATUS
approved