A182691 Composite Beatty sequence of sqrt(2).

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

Offset: 1

Author

Clark Kimberling, Nov 27 2010

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A001951, A001952, A107857.

Programs

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 *)

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).