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

Author

Clark Kimberling, Nov 26 2010

Keywords

• nonn

Comments

Let S be the set generated by these rules: (1) if m and n are in S and m

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.

Crossrefs

Cf. A182653, A182655, A182656.

Programs

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) ;

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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