A288507 Least number k such that both prime(k+1) -/+ prime(k) are products of n prime factors (counting multiplicity).

24, 319, 738, 57360, 1077529, 116552943

Offset

3,1

Comments

Prime(k) + prime(k+1) cannot be semiprime, so the offset is 3.

For n=3 to 8, all terms k happen to satisfy prime(k+1) - prime(k) = 2^n. - Michel Marcus, Jul 24 2017

Links

Table of n, a(n) for n=3..8.

Example

n = 8: k = 116552943, p = prime(k) = 2394261637, q = prime(k+1) = 2394261893; both q-p = 2^8 and  p+q = 2*3^2*5*7^3*155119 are 8-almost primes (A046310).

Prog

(PARI) a(n) = my(k = 1, p = 2, q = nextprime(p+1)); while((bigomega(p+q)!= n) || (bigomega(p-q)!= n), k++; p = q; q = nextprime(p+1)); k; \\ Michel Marcus, Jul 24 2017
(Python)
from sympy import factorint, nextprime
def A288507(n):
    k, p, q = 1, 2, 3
    while True:
        if sum(factorint(q-p).values()) == n and sum(factorint(q+p).values()) == n:
            return k
        k += 1
        p, q = q, nextprime(q) # Chai Wah Wu, Jul 23 2017

Crossrefs

Cf. A001043, A001223, A046310, A251600.

Sequence in context: A004413 A319554 A069779 * A199301 A239793 A289706

Adjacent sequences: A288504 A288505 A288506 * A288508 A288509 A288510

Keyword

nonn,more

Author

Zak Seidov, Jun 10 2017

Status

approved