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

1, 2, 4, 7, 8, 11, 12, 14, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 65, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 82, 83, 84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 98, 100

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) 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.

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.

Links

Table of n, a(n) for n=1..69.

Maple

A182654 := proc(amax)
        a := {1, 2} ;
        r := sqrt(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:
A182654(100) ;

Crossrefs

Cf. A182653, A182655, A182656.

Sequence in context: A094599 A050082 A209864 * A112648 A307284 A323108

Adjacent sequences: A182651 A182652 A182653 * A182655 A182656 A182657

Keyword

nonn

Author

Clark Kimberling, Nov 26 2010

Status

approved