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

1,3

Comments

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

Links

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

Example

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.

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]);

Prog

(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

Crossrefs

Cf. A023219, A340439.

Sequence in context: A088555 A040178 A089719 * A109550 A040991 A089721

Adjacent sequences: A340441 A340442 A340443 * A340445 A340446 A340447

Keyword

nonn,look

Author

Robert Israel, Jan 07 2021

Status

approved