

A276877


Sumscomplement of the Beatty sequence for Pi.


2



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
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OFFSET

1,2


COMMENTS

See A276871 for a definition of sumscomplement 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 * A078608 A189934 A189386
Adjacent sequences: A276874 A276875 A276876 * A276878 A276879 A276880


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Sep 27 2016


STATUS

approved



