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A276877 Sums-complement 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 (list; graph; refs; listen; history; text; internal format)
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 * A078608 A189934 A189386

Adjacent sequences:  A276874 A276875 A276876 * A276878 A276879 A276880

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 27 2016

STATUS

approved

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Last modified December 12 00:07 EST 2018. Contains 318052 sequences. (Running on oeis4.)