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A182691 Composite Beatty sequence of sqrt(2). 1
3, 4, 13, 18, 61, 86, 293, 414, 1413, 1998, 6821, 9646, 32933, 46574, 159013, 224878, 767781, 1085806, 3707173, 5242734, 17899813, 25314158, 86427941, 122227566, 417311013, 590166894, 2014955813, 2849577838, 9729067301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The bisection (4,18,86,...) is a subsequence of A001951.

The bisection (3,13,61,...) is a subsequence of A001952.

See the comment at A107857 regarding Beatty sequences.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = floor(s*a(n-1)) if n odd, a(n)=floor(r*a(n-1)) if n even, where r=sqrt(2), s=2+r, a(1)=floor(s).

EXAMPLE

a(1)=floor(2+sqrt(2))=3, a(2)=floor(r*a(1))=4.

MAPLE

Digits := 16 ;

A182691 := proc(n) option remember; local r, s ; r := sqrt(2) ; s := 2+r ; if n = 1 then floor(s) ; elif type(n, 'odd') then floor(s*procname(n-1)) ; else floor(r*procname(n-1)) ; end if; end proc:

seq(A182691(n), n=1..30) ;

MATHEMATICA

a[1]:= 3; a[n_]:= If[OddQ[n], Floor[(2+Sqrt[2])*a[n-1]], Floor[Sqrt[2]*a[n-1]]]; Table[a[n], {n, 1, 50}] (* G. C. Greubel, Sep 29 2018 *)

CROSSREFS

Cf. A001951, A001952, A107857.

Sequence in context: A205901 A302392 A293941 * A026700 A187775 A295955

Adjacent sequences:  A182688 A182689 A182690 * A182692 A182693 A182694

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 27 2010

STATUS

approved

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Last modified July 29 11:51 EDT 2021. Contains 346346 sequences. (Running on oeis4.)