The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182655 Floor-sum sequence of r, with r=(3+sqrt(5))/2 and a(1)=1, a(2)=2. 3

%I #7 Mar 30 2012 18:57:12

%S 1,2,7,20,23,54,57,62,65,70,78,112,143,146,151,154,159,164,167,172,

%T 175,180,185,188,193,201,206,209,214,222,230,235,243,256,264,290,295,

%U 298,303,311,319,324,332,345,353,366

%N Floor-sum sequence of r, with r=(3+sqrt(5))/2 and a(1)=1, a(2)=2.

%C Let S be the set generated by these rules: (1) if m and n are in S and m<n, then floor(mr+nr) is in S; (2) two or more specific numbers are in S. The floor-sum sequence determined by (1) and (2) results by arranging the elements of S in strictly increasing order.

%C Let B be the Beatty sequence of r. Then a floor-sum sequence of r is a subsequence of B if and only if a(1) and a(2) are terms of B.

%e 7 is in the sequence because floor(r*a(1)+r*a(2))=floor(r+2r)=7

%e 57 is in the sequence because floor(r*a(2)+r*a(4))=floor(r*22)=57

%e 61 is not in the sequence because 23*r=60.21... and 24*r=62.83... so there are no integers x,y with floor(r*(x+y))=61

%e 60 is not in the sequence because floor(r*(x+y))=60 requires x+y=23, and no pair of elements of the sequence sum to 23

%Y Cf. A182653, A182654, A182656. A001950.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 26 2010

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 15:00 EDT 2024. Contains 372826 sequences. (Running on oeis4.)