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A276879 Sums-complement of the Beatty sequence for 1 + sqrt(2).

%I A276879 #13 Sep 10 2023 01:50:56
%S A276879 1,6,11,18,23,30,35,40,47,52,59,64,69,76,81,88,93,100,105,110,117,122,
%T A276879 129,134,139,146,151,158,163,170,175,180,187,192,199,204,209,216,221,
%U A276879 228,233,238,245,250,257,262,269,274,279,286,291,298,303,308,315
%N A276879 Sums-complement of the Beatty sequence for 1 + sqrt(2).
%C A276879 See A276871 for a definition of sums-complement and guide to related sequences.
%H A276879 G. C. Greubel, <a href="/A276879/b276879.txt">Table of n, a(n) for n = 1..5000</a>
%H A276879 Robbert Fokkink, <a href="https://arxiv.org/abs/2309.01644">The Pell Tower and Ostronometry</a>, arXiv:2309.01644 [math.CO], 2023.
%H A276879 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%e A276879 The Beatty sequence for 1 + sqrt(2) is A003151 = (0,2,4,7,9,12,14,16,...), with difference sequence s = A276862 = (2,2,3,2,3,2,2,3,2,3,2,2,3,2,3,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,12,...), with complement (1,6,11,18,23,...).
%t A276879 z = 500; r = 1+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A003151 *)
%t A276879 t = Differences[b]; (* A276862 *)
%t A276879 c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
%t A276879 u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
%t A276879 w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w]  (* A276879 *)
%Y A276879 Cf. A003151, A276862, A276871.
%K A276879 nonn,easy
%O A276879 1,2
%A A276879 _Clark Kimberling_, Sep 27 2016