The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A079936 Greedy frac multiples of sqrt(5): a(1)=1, sum(n>0,frac(a(n)*x))=1 at x=sqrt(5). 2
 1, 2, 5, 13, 17, 34, 305, 610, 1597, 4181, 5473, 10946, 98209, 196418, 514229, 1346269, 1762289, 3524578, 31622993, 63245986, 165580141, 433494437, 567451585, 1134903170, 10182505537, 20365011074, 53316291173, 139583862445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The n-th greedy frac multiple of x is the smallest integer that does not cause sum(k=1..n,frac(a(k)*x)) to exceed unity; an infinite number of terms appear as the denominators of the convergents to the continued fraction of x. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,322,0,0,0,0,0,-1). FORMULA For n>=0, a(6n+1)=A001076(4n+1); a(6n+2)=2a(6n+1); a(6n+3)=A001076(4n+1)+A001076(4n+2); a(6n+4)=A001076(4n+3)-A001076(4n+2); a(6n+5)=A001076(4n+3); a(6n+6)=2a(6n+5). Asymptotics: a(6n) -> 2*sqrt(5)*(tau)^(12n-3); a(6n+2)/a(6n+1) -> (tau)^2; a(6n+3)/a(6n+2) -> (tau)^2; a(6n+4)/a(6n+3) -> (tau)^2/2; a(6n+6)/a(6n+5) -> (tau)^6/2; where tau = (1+sqrt(5))/2. G.f.: -x*(x -1)*(2*x^10 +3*x^9 +8*x^8 +21*x^7 +55*x^6 +72*x^5 +38*x^4 +21*x^3 +8*x^2 +3*x +1) / (x^12 -322*x^6 +1). - Colin Barker, Jun 16 2013 EXAMPLE a(4) = 13 since frac(1x) + frac(2x) + frac(5x) + frac(13x) < 1, while frac(1x) + frac(2x) + frac(5x) + frac(k*x) > 1 for all k>5 and k<13. CROSSREFS Cf. A001076 (denominators of convergents to sqrt(5)), A079934, A079935, A079937. Sequence in context: A087952 A124255 A293173 * A102854 A156009 A215275 Adjacent sequences:  A079933 A079934 A079935 * A079937 A079938 A079939 KEYWORD nonn,easy AUTHOR Benoit Cloitre and Paul D. Hanna, Jan 21 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 22 14:30 EDT 2021. Contains 343177 sequences. (Running on oeis4.)