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A276882
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Sums-complement of the Beatty sequence for 2 + sqrt(2).
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3
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1, 2, 5, 8, 9, 12, 15, 16, 19, 22, 25, 26, 29, 32, 33, 36, 39, 42, 43, 46, 49, 50, 53, 56, 57, 60, 63, 66, 67, 70, 73, 74, 77, 80, 83, 84, 87, 90, 91, 94, 97, 98, 101, 104, 107, 108, 111, 114, 115, 118, 121, 124, 125, 128, 131, 132, 135, 138, 141, 142, 145
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OFFSET
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1,2
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COMMENTS
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See A276871 for a definition of sums-complement and guide to related sequences.
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LINKS
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EXAMPLE
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The Beatty sequence for 2 + sqrt(2) is A001952 = (0,3,6,10,13,17,20, 23,27,...), with difference sequence s = A276864 = (3,3,4,3,4,3,3,4,3,4,3,3,4,3,4,...). The sums s(j)+s(j+1)+...+s(k) include (3,4,6,7,10,11,13,14,17,...), with complement (1,2,5,8,9,12,15,...).
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MATHEMATICA
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z = 500; r = 2+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A001952 *)
c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w] (* A276882 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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