A276877 Sums-complement of the Beatty sequence for Pi.

1, 2, 5, 8, 11, 14, 17, 20, 23, 24, 27, 30, 33, 36, 39, 42, 45, 46, 49, 52, 55, 58, 61, 64, 67, 68, 71, 74, 77, 80, 83, 86, 89, 90, 93, 96, 99, 102, 105, 108, 111, 112, 115, 118, 121, 124, 127, 130, 133, 134, 137, 140, 143, 146, 149, 152, 155, 156, 159, 162

Offset

1,2

Comments

See A276871 for a definition of sums-complement and guide to related sequences.

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to Beatty sequences

Example

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,...).

Mathematica

z = 500; r = Pi; b = Table[Floor[k*r], {k, 0, z}]; (* A022844 *)
t = Differences[b]; (* A063438 *)
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]  (* A276877 *)

Crossrefs

Cf. A022844, A063438, A276871.

Sequence in context: A064718 A190336 A276889 * A329961 A078608 A329988

Adjacent sequences: A276874 A276875 A276876 * A276878 A276879 A276880

Keyword

nonn,easy

Author

Clark Kimberling, Sep 27 2016

Status

approved