This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182691 #10 Sep 30 2018 20:21:05
%S A182691 3,4,13,18,61,86,293,414,1413,1998,6821,9646,32933,46574,159013,
%T A182691 224878,767781,1085806,3707173,5242734,17899813,25314158,86427941,
%U A182691 122227566,417311013,590166894,2014955813,2849577838,9729067301
%N A182691 Composite Beatty sequence of sqrt(2).
%C A182691 The bisection (4,18,86,...) is a subsequence of A001951.
%C A182691 The bisection (3,13,61,...) is a subsequence of A001952.
%C A182691 See the comment at A107857 regarding Beatty sequences.
%H A182691 G. C. Greubel, <a href="/A182691/b182691.txt">Table of n, a(n) for n = 1..1000</a>
%F A182691 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).
%e A182691 a(1)=floor(2+sqrt(2))=3, a(2)=floor(r*a(1))=4.
%p A182691 Digits := 16 ;
%p A182691 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:
%p A182691 seq(A182691(n),n=1..30) ;
%t A182691 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 *)
%Y A182691 Cf. A001951, A001952, A107857.
%K A182691 nonn
%O A182691 1,1
%A A182691 _Clark Kimberling_, Nov 27 2010