A175835 Number of real roots of the polynomial Sum_{k=0..n-1} A001620(1+k-n)*x^k, whose coefficients are the decimal digits of the Euler-Mascheroni constant.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 0, 3, 0, 3, 4, 1, 4, 1, 0, 1

Offset: 1

Author

Michel Lagneau, Dec 05 2010

Keywords

• nonn
• base
• less

Comments

a(n) = number of real zeros of the polynomial P(n,x) = Sum_{k=0..n-1} g(k) x^k, where g(k) are the digits of the decimal expansion of floor(gamma*10^n), g(k)=A001620(k-n).

Examples

			a(4)=1 because 5772 = A139260(4) => P(4,x) = 2 + 7x + 7x^2 +  5x^3 has 1 real root near -0.4.
		

Crossrefs

Cf. A173667, A001620.

Programs

Maple

A139260 := proc(n) floor(gamma*10^n) ;end proc:
A175835 := proc(n) local edgs ; edgs := convert(A139260(n),base,10) ; add(op(i,edgs)*x^(i-1),i=1..nops(edgs)) ; [fsolve(%,x,real)] ; nops(%) ; end proc:
seq(A175835(n),n=1..20) ; # R. J. Mathar, Dec 11 2010