A027919 - OEIS

%I #12 Dec 10 2019 20:04:48

%S 2,4,6,8,11,13,16,19,22,25,29,32,36,39,43,47,51,56,60,64,69,74,78,83,

%T 88,93,98,103,109,114,119,125,131,136,142,148,154,160,166,172,178,185,

%U 191,198,204,211,217,224,231,238,245,252,259,266

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

%F a(n) = min{k: A000914(k) >= A001303(n-2)}. - _Sean A. Irvine_, Dec 10 2019

%p SymmPolyn := proc(L::list,n::integer)

%p     local c,a,sel;

%p     a :=0 ;

%p     sel := combinat[choose](nops(L),n) ;

%p     for c in sel do

%p         a := a+mul(L[e],e=c) ;

%p     end do:

%p     a;

%p end proc:

%p A027919 := proc(n)

%p      local k,i;

%p      [seq(i,i=1..n)] ;

%p     e3 := SymmPolyn(%,3) ;

%p     for k from 1 do

%p         [seq(i,i=1..k+1)] ;

%p         if SymmPolyn(%,2) >= e3 then

%p             return k;

%p         end if;

%p     end do:

%p end proc: # _R. J. Mathar_, Sep 23 2016

%Y Cf. A000914, A001303.

%K nonn

%O 3,1

%A _Clark Kimberling_

%E Definition modified by _R. J. Mathar_, Sep 23 2016