A027919 a(n) = least k such that 2nd elementary symmetric function of {1,2,...,k+1} >= 3rd elementary symmetric function of {1,2,...,n}.

2, 4, 6, 8, 11, 13, 16, 19, 22, 25, 29, 32, 36, 39, 43, 47, 51, 56, 60, 64, 69, 74, 78, 83, 88, 93, 98, 103, 109, 114, 119, 125, 131, 136, 142, 148, 154, 160, 166, 172, 178, 185, 191, 198, 204, 211, 217, 224, 231, 238, 245, 252, 259, 266

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A000914, A001303.

Programs

Maple

SymmPolyn := proc(L::list,n::integer)
    local c,a,sel;
    a :=0 ;
    sel := combinat[choose](nops(L),n) ;
    for c in sel do
        a := a+mul(L[e],e=c) ;
    end do:
    a;
end proc:
A027919 := proc(n)
     local k,i;
     [seq(i,i=1..n)] ;
    e3 := SymmPolyn(%,3) ;
    for k from 1 do
        [seq(i,i=1..k+1)] ;
        if SymmPolyn(%,2) >= e3 then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Sep 23 2016

Formula

a(n) = min{k: A000914(k) >= A001303(n-2)}. - Sean A. Irvine, Dec 10 2019

Extensions

Definition modified by R. J. Mathar, Sep 23 2016