|
%I #17 Aug 07 2016 20:42:41
%S 1,10,45,64,369,948,1155,9687,22998,126291,174997,1299997,4452157,
%T 6463650,29499996,69999996,888398929,4549999995,38445656295,
%U 454999999995,683977034682,699999999994,29499999999994,45426425047212,129999999999993,267746023852371,579369695158668
%N Integers of the form Sum_{k=1..m} d(k), where d(k) is the decimal fraction 0.k (e.g. d(999)=0.999).
%C These are the sums arising in A054464.
%H Robert Israel, <a href="/A275623/b275623.txt">Table of n, a(n) for n = 1..1793</a>
%F From _Robert Israel_, Aug 07 2016: (Start)
%F For d >=2, the m with d digits are the solutions of x^2 + x - 9*10^(d-1)*d - 10^(d-1) == 0 (mod 2*10^d) with 10^(d-1) <= x < 10^d.
%F The corresponding a(n) are m(m+1)10^(-d)/2 + (10^d-9d-1)/20. (End)
%p T:= (x, d) -> ((1/2)*x^2+(1/2)*x)*10^(-d)-(9/20)*d+(1/20)*10^d-1/20:
%p F:= proc(d) local x, S;
%p S:= map(t -> subs(t, x), [msolve(x^2 + x - 9*10^(d-1)*d - 10^(d-1), 2*10^d)]);
%p op(map(T, sort(select(t -> t >= 10^(d-1) and t < 10^d, S)), d))
%p end proc:
%p [1,op(map(F, [$2..30]))]; # _Robert Israel_, Aug 07 2016
%Y Cf. A054464, A275572.
%K nonn,base
%O 1,2
%A _N. J. A. Sloane_, Aug 07 2016
|
