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

1,11

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).

Links

Table of n, a(n) for n=1..42.

Example

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

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

Crossrefs

Cf. A173667, A001620.

Sequence in context: A355402 A275344 A206826 * A123738 A194511 A214526

Adjacent sequences: A175832 A175833 A175834 * A175836 A175837 A175838

Keyword

nonn,base,less

Author

Michel Lagneau, Dec 05 2010

Status

approved