A356271 Prime numbers in the sublists defined in A348168 that contain a single prime.

2, 3, 5, 7, 23, 53, 89, 157, 173, 211, 293, 353, 359, 409, 449, 683, 691, 839, 919, 977, 983, 1039, 1069, 1103, 1109, 1201, 1223, 1237, 1283, 1327, 1381, 1439, 1459, 1511, 1613, 1627, 1637, 1709, 2039, 2099, 2179, 2213, 2221, 2243, 2251, 2273, 2447, 2633, 2917

Offset: 1

Author

Ya-Ping Lu, Aug 01 2022

Keywords

• nonn

Comments

It seems that lim_{n->oo} n/primepi(a(n)) = 0.102 approximately.

Crossrefs

Cf. A348168.

Programs

Python

from sympy import nextprime; R = [2]; p0 = 2
while len(R) < 50:
    p1 = nextprime(p0); p = nextprime(p1); g1 = p - p1
    if g1 >= p1 - p0: R.append(p1)
    else:
        while p - p1 <= g1: p1 = p; p = nextprime(p)
    p0 = p1
print(*R, sep = ', ')