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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.
1
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).
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
Sequence in context: A355402 A275344 A206826 * A123738 A194511 A214526
KEYWORD
nonn,base,less
AUTHOR
Michel Lagneau, Dec 05 2010
STATUS
approved