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A276884 Sums-complement of the Beatty sequence for 2 + sqrt(5).

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%I A276884 #10 Jan 30 2017 02:49:49
%S A276884 1,2,3,6,7,10,11,14,15,18,19,20,23,24,27,28,31,32,35,36,37,40,41,44,
%T A276884 45,48,49,52,53,54,57,58,61,62,65,66,69,70,71,74,75,78,79,82,83,86,87,
%U A276884 90,91,92,95,96,99,100,103,104,107,108,109,112,113,116,117
%N A276884 Sums-complement of the Beatty sequence for 2 + sqrt(5).
%C A276884 See A276871 for a definition of sums-complement and guide to related sequences.
%H A276884 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%e A276884 The Beatty sequence for 2 + sqrt(5) is A004976 = (0,4,8,12,16,21,25,29, 33,38,42,46,50,55,59,63,...) with difference sequence s = A276866 = (4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,...).  The sums s(j)+s(j+1)+...+s(k) include (4,5,8,9,12,13,16,...), with complement (1,2,3,6,7,10,11,14,...). - corrected by _Michel Dekking_, Jan 30 2017
%t A276884 z = 500; r = 2 + Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004076 *)
%t A276884 t = Differences[b]; (* A276866 *)
%t A276884 c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
%t A276884 u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
%t A276884 w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w];  (* A276884 *)
%Y A276884 Cf. A004976, A276866, A276871.
%K A276884 nonn,easy
%O A276884 1,2
%A A276884 _Clark Kimberling_, Oct 01 2016