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A276874 Sums-complement of the Beatty sequence for sqrt(8). 3

%I #7 Sep 30 2016 13:22:34

%S 1,4,7,10,13,18,21,24,27,30,35,38,41,44,47,52,55,58,61,64,69,72,75,78,

%T 81,86,89,92,95,100,103,106,109,112,117,120,123,126,129,134,137,140,

%U 143,146,151,154,157,160,163,168,171,174,177,180,185,188,191,194

%N Sums-complement of the Beatty sequence for sqrt(8).

%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 sqrt(8) is A022842 = (0,2,5,8,11,14,16,...), with difference sequence s = A276858 = (2,3,3,3,3,2,3,3,3,3,3,2,3,3,3,3,3,2,3,...). The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,11,12, 14,...), with complement (1,4,7,10,13,18,...)

%t z = 500; r = Sqrt[8]; b = Table[Floor[k*r], {k, 0, z}]; (* A022842 *)

%t t = Differences[b]; (* A276858 *)

%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] (* A276874 *)

%Y Cf. A022842, A276858, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 27 2016

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