OFFSET
1,1
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) 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.
LINKS
Iain Fox, Table of n, a(n) for n = 1..3000
EXAMPLE
a(3) = floor(2r+3r) = 8.
MAPLE
A182670 := proc(amax)
a := {2, 3} ;
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:
A182670(140) ;
PROG
(PARI) lista(nn) = my(S=[2, 3], r=(1+sqrt(5))/2, new, k); while(1, new=[]; for(m=1, #S, for(n=m+1, #S, k=floor(r*(S[m]+S[n])); if(k<=nn, new=setunion(new, [k])))); if(S==setunion(S, new), return(S)); S=setunion(S, new)) \\ Iain Fox, Apr 25 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 27 2010
STATUS
approved