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%I #6 Sep 30 2016 13:23:05
%S 1,2,5,8,11,14,17,20,23,24,27,30,33,36,39,42,45,46,49,52,55,58,61,64,
%T 67,68,71,74,77,80,83,86,89,90,93,96,99,102,105,108,111,112,115,118,
%U 121,124,127,130,133,134,137,140,143,146,149,152,155,156,159,162
%N Sums-complement of the Beatty sequence for Pi.
%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 Pi is A022844 = (0,3,6,9,12,15,18,21,25,,...), with difference sequence s = A063438 = (3,3,3,3,3,3,3,4,3,3,3,...). 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,...).
%t z = 500; r = Pi; b = Table[Floor[k*r], {k, 0, z}]; (* A022844 *)
%t t = Differences[b]; (* A063438 *)
%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] (* A276877 *)
%Y Cf. A022844, A063438, A276871.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Sep 27 2016
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