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Sums-complement of the Beatty sequence for 2e.
4

%I #6 Sep 30 2016 13:22:57

%S 1,2,3,4,7,8,9,12,13,14,15,18,19,20,23,24,25,26,29,30,31,34,35,36,37,

%T 40,41,42,45,46,47,50,51,52,53,56,57,58,61,62,63,64,67,68,69,72,73,74,

%U 75,78,79,80,83,84,85,88,89,90,91,94,95,96,99,100,101,102

%N Sums-complement of the Beatty sequence for 2e.

%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 2e is A276853 = (0,5,10,16,21,27,32,...), with difference sequence s = A276860 = (5,5,6,5,6,5,6,5,5,6,5,6,5,6,5,5,...). The sums s(j)+s(j+1)+...+s(k) include (5,6,7,10,11,16,17,...), with complement (1,2,3,4,7,8,9,12,...).

%t z = 500; r = 2E; b = Table[Floor[k*r], {k, 0, z}]; (* A276853 *)

%t t = Differences[b]; (* A276860 *)

%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] (* A276876 *)

%Y Cf. A276853, A276860, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 27 2016