

A182653


Floorsum 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 floorsum
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 floorsum 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



