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A276862 First differences of the Beatty sequence A003151 for 1 + sqrt(2). 5
2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjectures: equals A245219, and equals A097509. - Michel Dekking, Feb 18 2020

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..9999 [Offset adapted by Georg Fischer, Mar 07 2020]

FORMULA

a(n) = floor((n+1)*r) - floor(n*r) = A003151(n+1)-A003151(n), where r = 1 + sqrt(2), n >= 1.

a(n) = 1 + A006337(n) for n >+ 1. - R. J. Mathar, Sep 30 2016

MATHEMATICA

z = 500; r = 1+Sqrt[2]; b = Table[Floor[k*r], {k, 0, z}]; (* A003151 *)

Differences[b] (* A276862 *)

PROG

(PARI) vector(100, n, floor((n+1)*(1 + sqrt(2))) - floor(n*(1+sqrt(2)))) \\ G. C. Greubel, Aug 16 2018

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

CROSSREFS

Cf. A003151, A276879.

Sequence in context: A023397 A258115 A296658 * A175066 A066102 A036048

Adjacent sequences:  A276859 A276860 A276861 * A276863 A276864 A276865

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 24 2016

EXTENSIONS

Corrected by Michel Dekking, Feb 18 2020

STATUS

approved

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Last modified September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)