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A182653 Floor-sum sequence of r with r = golden ratio = (1+sqrt(5))/2 and a(1)=1, a(2)=2. 6
1, 2, 4, 8, 9, 14, 16, 17, 19, 21, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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) one or

more specific numbers are in S by decree.  The floor-sum

sequence determined by (1) and (2) results by arranging

the elements of S in strictly increasing order.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

Viewing the floor-sum as a binary operation o, we

create S in successive generations:

1, 2 (0th generation)

1o2=4 (1st generation)

1o4=8, 2o4=9 (2nd generation)

1o8=14, 2o8=16, 4o8=19 and four others (3rd generation)

MAPLE

A182653 := proc(amax)

        a := {1, 2} ; r := (1+sqrt(5))/2 ;

        while true do

                anew := {} ;

                for i in a do

                for j in a do

                        if i <> j then

                                S := floor(r*(i+j)) ;

                                if is(S <= amax) then

                                        anew := anew union { S };

                                end if;

                        end if;

                end do:

                end do:

                if a union anew = a then

                        return sort(a) ;

                end if;

                a := a union anew ;

        end do:

end proc:

A182653(106) ;

CROSSREFS

Cf. A182654, A182655, A182656.

Sequence in context: A115813 A048300 A178953 * A036349 A155562 A048715

Adjacent sequences:  A182650 A182651 A182652 * A182654 A182655 A182656

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 26 2010

STATUS

approved

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Last modified July 26 00:44 EDT 2017. Contains 289798 sequences.