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Revision History for A286655

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A286655

Characteristic sequence of the Beatty sequence, A022842, of sqrt(8).
(history; published version)

#8 by Michael De Vlieger at Thu Sep 01 19:47:57 EDT 2022

STATUS

reviewed

approved

#7 by Kevin Ryde at Thu Sep 01 19:37:37 EDT 2022

STATUS

proposed

reviewed

#6 by Georg Fischer at Thu Sep 01 14:36:59 EDT 2022

STATUS

editing

proposed

#5 by Georg Fischer at Thu Sep 01 14:36:53 EDT 2022

FORMULA

a(n) = 1 - floor((n+1)/*(1-1/r) ) + floor(n*(1-1/r)), where r = sqrt(8). [corrected by _Georg Fischer_, Sep 01 2022]

STATUS

approved

editing

#4 by N. J. A. Sloane at Fri May 12 00:16:29 EDT 2017

STATUS

proposed

approved

#3 by Clark Kimberling at Thu May 11 21:34:17 EDT 2017

STATUS

editing

proposed

#2 by Clark Kimberling at Thu May 11 21:31:13 EDT 2017

NAME

allocated for Clark KimberlingCharacteristic sequence of the Beatty sequence, A022842, of sqrt(8).

DATA

0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0

OFFSET

1

COMMENTS

The positions of 0 are given by A286323, and of 1, by A022842.

LINKS

Clark Kimberling, <a href="/A286655/b286655.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

a(n) = 1 - floor((n+1)/(1-1/r) + floor(n(1-1/r)), where r = sqrt(8).

MATHEMATICA

r = Sqrt[8];

s = 1 - Table[Floor[(n + 1) (1 - 1/r) - Floor[n (1 - 1/r)]], {n, 1, 200}] (* A286655 *)

Flatten[Position[s, 0]] (* A286323 *)

Flatten[Position[s, 1]] (* A022842 *)

CROSSREFS

Cf. A022842, A286323.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, May 11 2017

STATUS

approved

editing

#1 by Clark Kimberling at Thu May 11 20:36:17 EDT 2017

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved