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%I #10 Jul 27 2024 02:53:49
%S 1,4,7,12,15,18,23,26,31,34,37,42,45,50,53,56,61,64,69,72,75,80,83,88,
%T 91,94,99,102,105,110,113,118,121,124,129,132,137,140,143,148,151,156,
%U 159,162,167,170,175,178,181,186,189,194,197,200,205,208,211,216
%N Sums-complement of the Beatty sequence for e.
%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 e is A022843 = (0,2,5,8,10,13,16,...), with difference sequence s = A276859 = (2,3,3,2,3,3,3,2,3,3,2,3,3,3,2,...). The sums s(j)+s(j+1)+...+s(k) include (2,3,5,6,8,9,10,12,13,...), with complement (1,4,7,12,15,...).
%t z = 500; r = E; b = Table[Floor[k*r], {k, 0, z}]; (* A022843 *)
%t t = Differences[b]; (* A276859 *)
%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] (* A276875 *)
%Y Cf. A022843, A276859, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 27 2016
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