A340444 a(n) is the least prime of the form p*q + p*r + q*r where p is the n-th prime and q and r are primes < p, or 0 if there are none.

0, 0, 31, 41, 61, 71, 151, 101, 199, 151, 227, 191, 211, 311, 241, 271, 487, 311, 479, 653, 521, 401, 421, 727, 491, 823, 521, 541, 773, 571, 641, 661, 691, 701, 751, 761, 1109, 821, 2039, 1399, 1447, 911, 1543, 971, 991, 1607, 1061, 1571, 1831, 1151, 1171, 1201, 1697, 2273, 1291, 1321, 2711

Offset: 1

Author

Robert Israel, Jan 07 2021

Keywords

• nonn
• look

Comments

If prime(k) is in A023219, a(k) = 5*prime(k)+6.

Examples

			a(7) = 151 because prime(7) = 17, and 151 = 17*3+17*5+3*5 is the least prime of the form 17*p + 17*q + p*q.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A023219, A340439.

Programs

Maple

f:= proc(n) local p,L,i,j,t;
  p:= ithprime(n);
  L:= sort([seq(seq((ithprime(i)+p)*(ithprime(j)+p)-p^2, i=1..j-1),j=2..n-1)]);
  for t in L do if isprime(t) then return t fi od:
  0
end proc:
A:= map(f, [$1..100]);

Python

from sympy import isprime, prime
def aupto(nn):
  alst, plst = [0 for i in range(nn)], [prime(i+1) for i in range(nn)]
  for n in range(1, nn+1):
    p = plst[n-1]
    t = ((p, plst[i], plst[j]) for i in range(n-2) for j in range(i+1, n-1))
    for s in sorted(p*q + p*r + q*r for p, q, r in t):
      if isprime(s): alst[n-1]=s; break
  return alst
print(aupto(57)) # Michael S. Branicky, Jan 07 2021