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A361823 a(1) = 3; thereafter, a(n+1) is the smallest prime p such that p - prevprime(p) >= a(n) - prevprime(a(n)).

%I A361823 #17 Apr 23 2023 22:09:11
%S A361823 3,5,7,11,17,23,29,37,53,59,67,79,89,97,127,307,331,541,907,1151,1361,
%T A361823 8501,9587,12889,14143,15727,19661,25523,31469,156007,338119,360749,
%U A361823 370373,492227,1349651,1357333,1562051,2010881,4652507,11114087,15204131,17051887
%N A361823 a(1) = 3; thereafter, a(n+1) is the smallest prime p such that p - prevprime(p) >= a(n) - prevprime(a(n)).
%C A361823 a(n) is the leading prime in the (n+1)-th prime sublist defined in A348178.
%F A361823 a(n) = nextprime(A134266(n)). - _Michel Marcus_, Mar 30 2023
%o A361823 (Python)
%o A361823 from sympy import nextprime; q = 2; g = 0
%o A361823 while q < 20000000:
%o A361823     p = nextprime(q); d = p - q
%o A361823     if d >= g: print(p, end = ', '); g = d
%o A361823     q = p
%o A361823 (PARI) a361823(upto) = {my(pp=2, gap=1); forprime (p=3, upto, my(g=p-pp);if(g>=gap, print1(p,", "); gap=g); pp=p)};
%o A361823 a361823(20000000) \\ _Hugo Pfoertner_, Apr 03 2023
%Y A361823 Cf. A001223, A070866, A134266, A348178.
%K A361823 nonn
%O A361823 1,1
%A A361823 _Ya-Ping Lu_, Mar 25 2023