A357176 a(n) is the least prime that is the n-th elementary symmetric function of the first k primes for some k.

2, 31, 2101534937, 2927, 40361, 39075401846390482295581, 226026998201956974105518542793548663, 617651235401, 4325269278391458399931853204730438563, 12894795842691356733422939, 745410787149030809096434692201049325037186561467959704761393689387

Offset: 1

Author

Robert Israel, Sep 21 2022

Keywords

• nonn

Comments

a(n) is the first prime p such that (-1)^n*p is in the n-th column of A238146.

Examples

			a(4) = 2927 = 2*3*5*7 + 2*3*5*11 + 2*3*7*11 + 2*5*7*11 + 3*5*7*11 is the 4th symmetric function of the first 5 primes (2,3,5,7,11) and is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..118

Crossrefs

Cf. A238146.

Programs

Maple

N:= 20: V:= Vector(N):
S:= Vector(N): p:= 2: S[1]:= 2: V[1]:= 2: count:= 1:
while count < N do
  p:= nextprime(p);
  for k from N to 2 by -1 do
    S[k]:= S[k] + p*S[k-1];
    if V[k] = 0 and isprime(S[k]) then V[k]:= S[k]; count:= count+1; fi;
  od;
  S[1]:= S[1]+p;
od:
convert(V,list);