A356466 Prime numbers in the sublists defined in A348168 that contain exactly two primes.

11, 13, 17, 19, 29, 31, 59, 61, 79, 83, 127, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 197, 199, 239, 241, 331, 337, 347, 349, 397, 401, 419, 421, 431, 433, 439, 443, 521, 523, 541, 547, 673, 677, 701, 709, 787, 797, 809, 811, 821, 823, 827, 829

Offset: 1

Author

Ya-Ping Lu, Aug 08 2022

Keywords

• nonn

Comments

Let g = q - p be the gap between a pair of primes in the sequence, g < p - previprime(p) and g < nextprime(q) - q.

It seems that lim_{n-> oo} n/primepi(a(n)) = 0.314 approximately.

Crossrefs

Cf. A348168.

Programs

Python

from sympy import nextprime; R = []; p0 = 2
while len(R) < 60:
    p1 = nextprime(p0); M = [p1]; p = nextprime(p1); g1 = p - p1
    while g1 < p1 - p0 and p - p1 <= g1: M.append(p); p1 = p; p = nextprime(p)
    if len(M) == 2: R.extend(M)
    p0 = p1
print(*R, sep = ', ')