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%I #4 Oct 02 2016 00:36:49
%S 1,2,3,6,7,8,11,12,15,16,17,20,21,22,25,26,29,30,31,34,35,38,39,40,43,
%T 44,45,48,49,52,53,54,57,58,59,62,63,66,67,68,71,72,75,76,77,80,81,82,
%U 85,86,89,90,91,94,95,98,99,100,103,104,105,108,109,112
%N Sums-complement of the Beatty sequence for 3 + tau.
%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 3 + tau is A267855 = (-,4,9,13,18,23,27,...), with difference sequence s = A276868 = (4,5,4,5,5,4,5,4,5,5,4,5,5,4,5,4,...). The sums s(j)+s(j+1)+...+s(k) include (4,5,9,10,13,14,18,...), with complement (1,2,3,6,7,8,11,12,15,...).
%t z = 500; r = 3 + GoldenRatio; b = Table[Floor[k*r], {k, 0, z}]; (* A276855 *)
%t t = Differences[b]; (* A276868 *)
%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]; (* A276887 *)
%Y Cf. A276855, A276868, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Oct 01 2016
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