A027919 - OEIS

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

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OFFSET

3,1

LINKS

Table of n, a(n) for n=3..56.

FORMULA

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

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:

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

CROSSREFS

Cf. A000914, A001303.

Sequence in context: A022819 A081527 A070978 * A174058 A186382 A331417

Adjacent sequences: A027916 A027917 A027918 * A027920 A027921 A027922

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

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

STATUS

approved