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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).

%I A348178 #6 Oct 13 2021 10:34:27
%S A348178 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,
%T A348178 394,585,575,10972,14683,1762,743,9388,62587,551,14434,31184,176163,
%U A348178 407736,249427,111406,225524,1530229,4107702,3581556,116030,10028870,2065372
%N 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).
%C A348178 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).
%o A348178 (Python)
%o A348178 from sympy import nextprime
%o A348178 L = [2]
%o A348178 for n in range(1, 50):
%o A348178     print(len(L), end = ', ')
%o A348178     p0 = L[-1]; p1 = nextprime(p0); g0 = p1 - p0; M = [p1]; p = nextprime(p1)
%o A348178     while p - p1 < g0: M.append(p); p1 = p; p = nextprime(p)
%o A348178     L = M
%Y A348178 Cf. A085237, A134266, A348168.
%K A348178 nonn
%O A348178 1,5
%A A348178 _Ya-Ping Lu_, Oct 05 2021