A276883 - OEIS

%I #17 Nov 19 2024 04:33:24

%S 1,2,5,6,9,10,13,16,17,20,21,24,25,28,31,32,35,36,39,40,43,46,47,50,

%T 51,54,57,58,61,62,65,66,69,72,73,76,77,80,81,84,87,88,91,92,95,96,99,

%U 102,103,106,107,110,113,114,117,118,121,122,125,128,129,132

%N Sums-complement of the Beatty sequence for 2 + sqrt(3).

%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 2 + sqrt(3) is A003512 = (0,3,7,11,14,18,22,26,...), with difference sequence s = A276865 = (3,4,4,3,4,4,4,3,4,4,4,3,4,4,3,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,7,8,11,12,14,15,18,...), with complement (1,2,5,6,9,10,13,...).

%t z = 500; r = 2 + Sqrt[3]; b = Table[Floor[k*r], {k, 0, z}]; (* A003512 *)

%t t = Differences[b]; (* A276865 *)

%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]  (* A276883 *)

%Y Cf. A003512, A276865, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 27 2016