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A276876
Sums-complement of the Beatty sequence for 2e.
4
1, 2, 3, 4, 7, 8, 9, 12, 13, 14, 15, 18, 19, 20, 23, 24, 25, 26, 29, 30, 31, 34, 35, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 52, 53, 56, 57, 58, 61, 62, 63, 64, 67, 68, 69, 72, 73, 74, 75, 78, 79, 80, 83, 84, 85, 88, 89, 90, 91, 94, 95, 96, 99, 100, 101, 102
OFFSET
1,2
COMMENTS
See A276871 for a definition of sums-complement and guide to related sequences.
EXAMPLE
The Beatty sequence for 2e is A276853 = (0,5,10,16,21,27,32,...), with difference sequence s = A276860 = (5,5,6,5,6,5,6,5,5,6,5,6,5,6,5,5,...). The sums s(j)+s(j+1)+...+s(k) include (5,6,7,10,11,16,17,...), with complement (1,2,3,4,7,8,9,12,...).
MATHEMATICA
z = 500; r = 2E; b = Table[Floor[k*r], {k, 0, z}]; (* A276853 *)
t = Differences[b]; (* A276860 *)
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] (* A276876 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 27 2016
STATUS
approved