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A182654 Floor-sum sequence of r, with r=sqrt(2) and a(1)=1, a(2)=2. 4


%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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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)