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 A276884 Sums-complement of the Beatty sequence for 2 + sqrt(5). 3

%I

%S 1,2,3,6,7,10,11,14,15,18,19,20,23,24,27,28,31,32,35,36,37,40,41,44,

%T 45,48,49,52,53,54,57,58,61,62,65,66,69,70,71,74,75,78,79,82,83,86,87,

%U 90,91,92,95,96,99,100,103,104,107,108,109,112,113,116,117

%N Sums-complement of the Beatty sequence for 2 + sqrt(5).

%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(5) is A004976 = (0,4,8,12,16,21,25,29, 33,38,42,46,50,55,59,63,...) with difference sequence s = A276866 = (4,4,4,4,5,4,4,4,5,4,4,4,5,4,4,...). The sums s(j)+s(j+1)+...+s(k) include (4,5,8,9,12,13,16,...), with complement (1,2,3,6,7,10,11,14,...). - corrected by _Michel Dekking_, Jan 30 2017

%t z = 500; r = 2 + Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A004076 *)

%t t = Differences[b]; (* A276866 *)

%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]; (* A276884 *)

%Y Cf. A004976, A276866, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Oct 01 2016

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)