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%I #11 Jul 11 2023 08:30:36
%S 1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,
%T 0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,
%U 1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1
%N a(n) = [2*n*e] - 2*[n*e], where [ ] = floor and e is the natural logarithm base.
%C Suppose, in general, that a(n) = [(b*n+c)r] - b*[n*r] - [c*r]. If r > 0 and b and c are integers satisfying b >= 2 and 0 <= c <= b-1, then 0 <= a(n) <= b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1, 2, ..., b. These b+1 (or b) position sequences comprise a partition of the positive integers.
%t f[n_] := Floor[2 n*E] - 2*Floor[n*E];
%t t = Table[f[n], {n, 1, 220}] (* A190843 *)
%t Flatten[Position[t, 0]] (* A190847 *)
%t Flatten[Position[t, 1]] (* A190860 *)
%Y Cf. A001113 (e), A190847, A190860.
%K nonn,easy
%O 1
%A _Clark Kimberling_, May 26 2011
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