The On-Line Encyclopedia of Integer Sequences® (OEIS®)

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A276870

First differences of the Beatty sequence A110117 for sqrt(2) + sqrt(3).
(history; published version)

#9 by Charles R Greathouse IV at Thu Sep 08 08:46:17 EDT 2022

PROG

(MAGMAMagma) [Floor(n*(Sqrt(2) + Sqrt(3))) - Floor((n-1)*(Sqrt(2) + Sqrt(3))): n in [1..100]]; // G. C. Greubel, Aug 16 2018

Discussion
Thu Sep 08	08:46	OEIS Server: https://oeis.org/edit/global/2944

#8 by Alois P. Heinz at Thu Aug 16 19:19:09 EDT 2018

STATUS

proposed

approved

#7 by G. C. Greubel at Thu Aug 16 19:18:39 EDT 2018

STATUS

editing

proposed

#6 by G. C. Greubel at Thu Aug 16 19:18:33 EDT 2018

	COMMENTS	`a(n) = floor(nr) - floor(nr - r), where r = sqrt(2) + sqrt(3), n >= 1.`
	FORMULA	`a(n) = floor(nr) - floor(nr - r), where r = sqrt(2) + sqrt(3), n >= 1.`
	PROG	`(PARI) vector(100, n, floor(n(sqrt(2) + sqrt(3))) - floor((n-1)(sqrt(2)+sqrt(3)))) \\ G. C. Greubel, Aug 16 2018` `(MAGMA) [Floor(n(Sqrt(2) + Sqrt(3))) - Floor((n-1)(Sqrt(2) + Sqrt(3))): n in [1..100]]; // G. C. Greubel, Aug 16 2018`
	STATUS	`approved` `editing`

#5 by N. J. A. Sloane at Mon Sep 26 21:39:21 EDT 2016

STATUS

editing

approved

#4 by N. J. A. Sloane at Mon Sep 26 21:39:19 EDT 2016

NAME

DifferenceFirst sequencedifferences of the Beatty sequence A110117 for sqrt(2) + sqrt(3).

STATUS

proposed

editing

#3 by Clark Kimberling at Mon Sep 26 20:49:05 EDT 2016

STATUS

editing

proposed

#2 by Clark Kimberling at Mon Sep 26 20:46:20 EDT 2016

	NAME	`allocatedDifference sequence of the Beatty sequence A110117 for Clark Kimberlingsqrt(2) + sqrt(3).`
	DATA	`3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3`
	OFFSET	`1,1`
	COMMENTS	`a(n) = floor(nr) - floor(nr - r), where r = sqrt(2) + sqrt(3), n >= 1.`
	LINKS	`Clark Kimberling, <a href="/A276870/b276870.txt">Table of n, a(n) for n = 1..10000</a>`
	MATHEMATICA	`z = 500; r = Sqrt[2]+Sqrt[3]; b = Table[Floor[kr], {k, 0, z}] ( A110117 )` `Differences[b] ( A276870 *)`
	CROSSREFS	`Cf. A110117, A276889.`
	KEYWORD	`allocated` `nonn,easy`
	AUTHOR	`Clark Kimberling, Sep 26 2016`
	STATUS	`approved` `editing`

#1 by Clark Kimberling at Wed Sep 21 16:11:40 EDT 2016

	NAME	`allocated for Clark Kimberling`
	KEYWORD	`allocated`
	STATUS	`approved`

Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)