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

%I A027919 #12 Dec 10 2019 20:04:48
%S A027919 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 A027919 88,93,98,103,109,114,119,125,131,136,142,148,154,160,166,172,178,185,
%U A027919 191,198,204,211,217,224,231,238,245,252,259,266
%N A027919 a(n) = least k such that 2nd elementary symmetric function of {1,2,...,k+1} >= 3rd elementary symmetric function of {1,2,...,n}.
%F A027919 a(n) = min{k: A000914(k) >= A001303(n-2)}. - _Sean A. Irvine_, Dec 10 2019
%p A027919 SymmPolyn := proc(L::list,n::integer)
%p A027919     local c,a,sel;
%p A027919     a :=0 ;
%p A027919     sel := combinat[choose](nops(L),n) ;
%p A027919     for c in sel do
%p A027919         a := a+mul(L[e],e=c) ;
%p A027919     end do:
%p A027919     a;
%p A027919 end proc:
%p A027919 A027919 := proc(n)
%p A027919      local k,i;
%p A027919      [seq(i,i=1..n)] ;
%p A027919     e3 := SymmPolyn(%,3) ;
%p A027919     for k from 1 do
%p A027919         [seq(i,i=1..k+1)] ;
%p A027919         if SymmPolyn(%,2) >= e3 then
%p A027919             return k;
%p A027919         end if;
%p A027919     end do:
%p A027919 end proc: # _R. J. Mathar_, Sep 23 2016
%Y A027919 Cf. A000914, A001303.
%K A027919 nonn
%O A027919 3,1
%A A027919 _Clark Kimberling_
%E A027919 Definition modified by _R. J. Mathar_, Sep 23 2016