A276872 - OEIS

%I #4 Sep 26 2016 21:39:51

%S 1,6,11,16,21,28,33,38,43,50,55,60,65,70,77,82,87,92,99,104,109,114,

%T 119,126,131,136,141,148,153,158,163,168,175,180,185,190,197,202,207,

%U 212,217,224,229,234,239,246,251,256,261,268,273,278,283,288,295,300

%N Sums-complement of the Beatty sequence for sqrt(6).

%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(6) is A022840 = (0, 2, 4, 7, 9, 12, 14, 17,...), with difference sequence s = A276856 = (2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,10,12,...), with complement (1,6,11,16,21,...).

%t z = 500; r = Sqrt[6]; b = Table[Floor[k*r], {k, 0, z}]; (* A022840 *)

%t t = Differences[b]; (* A276856 *)

%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];  (* A276872 *)

%Y Cf. A022840, A276856, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 26 2016