|
%I #4 Oct 02 2016 00:36:54
%S 1,4,7,12,15,20,23,26,31,34,39,42,45,50,53,58,61,66,69,72,77,80,85,88,
%T 91,96,99,104,107,112,115,118,123,126,131,134,137,142,145,150,153,156,
%U 161,164,169,172,177,180,183,188,191,196,199,202,207,210,215,218
%N Sums-complement of the Beatty sequence for 2 + sqrt(1/2).
%C See A276871 for a definition of sums-complement and guide to related sequences.
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%e The Beatty sequence for 2 + sqrt(1/2) is A182969 = (0,2,5,8,10,13,16,18,21,...), with difference sequence s = A276869 = (2,3,3,2,3,3,2,3,3,3,2,3,3,2,3,3,3,2,...). The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,11,13,14,16,...), with complement (1,4,7,12,15,20,23,...).
%t z = 500; r = 2 + Sqrt[1/2]; b = Table[Floor[k*r], {k, 0, z}]; (* A182769 *)
%t t = Differences[b]; (* A276869 *)
%t c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
%t u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
%t w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w]; (* A276888 *)
%Y Cf. A182769, A276869, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 01 2016
|
