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%I #9 Mar 30 2012 18:57:12
%S 1,2,4,7,8,11,12,14,15,16,18,19,21,22,24,25,26,28,29,31,32,33,35,36,
%T 38,39,41,42,43,45,46,48,49,50,52,53,55,56,57,59,60,62,63,65,66,67,69,
%U 70,72,73,74,76,77,79,80,82,83,84,86,87,89,90,91,93,94,96,97,98,100
%N Floor-sum sequence of r, with r=sqrt(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. For example, 5 is A001951 but not in A182654.
%p A182654 := proc(amax)
%p a := {1,2} ;
%p r := sqrt(2) ;
%p while true do
%p anew := {} ;
%p for i in a do
%p for j in a do
%p if i <> j then S := floor(r*(i+j)) ; if is(S <= amax) then anew := anew union { S }; end if;
%p end if;
%p end do:
%p end do:
%p if a union anew = a then
%p return sort(a) ;
%p end if;
%p a := a union anew ;
%p end do:
%p end proc:
%p A182654(100) ;
%Y Cf. A182653, A182655, A182656.
%K nonn
%O 1,2
%A _Clark Kimberling_, Nov 26 2010
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