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A276881 Sums-complement of the Beatty sequence for 1 + sqrt(5). 4

%I

%S 1,2,5,8,11,14,15,18,21,24,27,28,31,34,37,40,41,44,47,50,53,54,57,60,

%T 63,66,69,70,73,76,79,82,83,86,89,92,95,96,99,102,105,108,109,112,115,

%U 118,121,124,125,128,131,134,137,138,141,144,147,150,151,154

%N Sums-complement of the Beatty sequence for 1 + 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 1 + sqrt(5) is A276854 = (0,3,6,9,12,16,19,...), with difference sequence s = A276863 = (3,3,3,3,4,3,3,3,4,3,3,3,4,3,3,3,4,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,9,10,12,13,...), with complement (1,2,5,8,11,14,15,,...).

%t z = 500; r = 1+ Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A276854 *)

%t t = Differences[b]; (* A276863 *)

%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] (* A276881 *)

%Y Cf. A276854, A276863, A276871.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 27 2016

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Last modified February 19 16:24 EST 2020. Contains 332045 sequences. (Running on oeis4.)