A348178 The list of all prime numbers is split into sublists with the 1st sublist L_1 = {2} and n-th sublist L_n = {p_1, p_2, ..., p_m}. a(n) is the largest m such that the maximum prime gap in L_n is < p_1 - prevprime(p_1).

1, 1, 1, 1, 2, 2, 1, 2, 4, 1, 2, 3, 2, 1, 6, 32, 4, 33, 55, 35, 28, 842, 124, 349, 131, 168, 394, 585, 575, 10972, 14683, 1762, 743, 9388, 62587, 551, 14434, 31184, 176163, 407736, 249427, 111406, 225524, 1530229, 4107702, 3581556, 116030, 10028870, 2065372

Offset: 1

Author

Ya-Ping Lu, Oct 05 2021

Keywords

• nonn

Comments

The last prime in the n-th sublist is A134266(n). The gap between the n-th and (n+1)-th sublists is A085237(n).

Crossrefs

Cf. A085237, A134266, A348168.

Programs

Python

from sympy import nextprime
L = [2]
for n in range(1, 50):
    print(len(L), end = ', ')
    p0 = L[-1]; p1 = nextprime(p0); g0 = p1 - p0; M = [p1]; p = nextprime(p1)
    while p - p1 < g0: M.append(p); p1 = p; p = nextprime(p)
    L = M