A340439 a(n) is the number of primes of the form p*q + p*r + q*r where p is the n-th prime and q and r are primes < p.

0, 0, 1, 3, 5, 7, 9, 12, 11, 16, 20, 23, 22, 32, 30, 34, 42, 53, 48, 49, 61, 62, 67, 66, 81, 73, 94, 94, 103, 105, 114, 112, 114, 142, 123, 153, 164, 155, 167, 170, 183, 196, 204, 228, 208, 235, 242, 231, 240, 254, 267, 246, 281, 269, 297, 306, 298, 340, 356, 338, 378, 339, 421, 363, 424, 386

Offset

1,4

Comments

A prime is counted only once even if it arises in several ways.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(6) = 7 because prime(6) = 13 and there are 7 such primes:
   71 = 2*3  + 2*13 +  3*13
  101 = 2*5  + 2*13 +  5*13
  131 = 2*7  + 2*13 +  7*13
  151 = 3*7  + 3*13 +  7*13
  191 = 5*7  + 5*13 +  7*13 = 2*11 + 2*13 + 11*13
  263 = 5*11 + 5*13 + 11*13
  311 = 7*11 + 7*13 + 11*13.

Maple

f:= proc(n) local i, j, t;
  nops(select(isprime, {seq(seq((ithprime(i)+ithprime(j))*ithprime(n)+ithprime(i)*ithprime(j), i=1..j-1), j=2..n-1)}))
end proc:
map(f, [$1..100]);

Prog

(Python)
from sympy import isprime, prime
def aupto(nn):
  alst, plst = [], [prime(i) for i in range(1, nn+1)]
  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))
    u = (p*q + p*r + q*r for p, q, r in t)
    alst.append(len(set(s for s in u if isprime(s))))
  return alst
print(aupto(66)) # Michael S. Branicky, Jan 07 2021

Crossrefs

Cf. A340444.

Sequence in context: A061512 A356750 A083964 * A131628 A079091 A353149

Adjacent sequences: A340436 A340437 A340438 * A340440 A340441 A340442

Keyword

nonn

Author

Robert Israel, Jan 07 2021

Status

approved