cp's OEIS Frontend

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

%I A357176 #59 Oct 02 2022 20:02:07
%S A357176 2,31,2101534937,2927,40361,39075401846390482295581,
%T A357176 226026998201956974105518542793548663,617651235401,
%U A357176 4325269278391458399931853204730438563,12894795842691356733422939,745410787149030809096434692201049325037186561467959704761393689387
%N A357176 a(n) is the least prime that is the n-th elementary symmetric function of the first k primes for some k.
%C A357176 a(n) is the first prime p such that (-1)^n*p is in the n-th column of A238146.
%H A357176 Robert Israel, <a href="/A357176/b357176.txt">Table of n, a(n) for n = 1..118</a>
%e A357176 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.
%p A357176 N:= 20: V:= Vector(N):
%p A357176 S:= Vector(N): p:= 2: S[1]:= 2: V[1]:= 2: count:= 1:
%p A357176 while count < N do
%p A357176   p:= nextprime(p);
%p A357176   for k from N to 2 by -1 do
%p A357176     S[k]:= S[k] + p*S[k-1];
%p A357176     if V[k] = 0 and isprime(S[k]) then V[k]:= S[k]; count:= count+1; fi;
%p A357176   od;
%p A357176   S[1]:= S[1]+p;
%p A357176 od:
%p A357176 convert(V,list);
%Y A357176 Cf. A238146.
%K A357176 nonn
%O A357176 1,1
%A A357176 _Robert Israel_, Sep 21 2022