A175835 - OEIS

%I #12 May 14 2019 22:02:17

%S 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,

%T 0,3,4,1,4,1,0,1

%N 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.

%C 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).

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

%p A139260 := proc(n) floor(gamma*10^n) ;end proc:

%p 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:

%p seq(A175835(n),n=1..20) ; # _R. J. Mathar_, Dec 11 2010

%Y Cf. A173667, A001620.

%K nonn,base,less

%O 1,11

%A _Michel Lagneau_, Dec 05 2010