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A063095 Record prime gap among first n+1 primes.

%I A063095 #12 Sep 11 2019 16:37:12
%S A063095 1,2,2,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,14,14,14,
%T A063095 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
%U A063095 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14
%N A063095 Record prime gap among first n+1 primes.
%D A063095 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.22, p. 249. (See G(x), which is an analog of pi(x).)
%H A063095 Chai Wah Wu, <a href="/A063095/b063095.txt">Table of n, a(n) for n = 1..10000</a>
%e A063095 A value of d in this sequence persists until a larger value arises. Note that values like 10, 12, 16 are never maximal. Distinct, increasing prime gaps are given in A005250.
%t A063095 Table[Max[Table[Prime[w+1]-Prime[w], {w, 1, j}]], {j, 1, 500}] a(n)= Max{p[j+1]-p[j]; j=1, ..n}
%o A063095 (Python)
%o A063095 from sympy import nextprime
%o A063095 def A063095(n):
%o A063095     c, p = 0, 2
%o A063095     for i in range(n):
%o A063095         q = nextprime(p)
%o A063095         c, p = max(c,q-p), q
%o A063095     return c # _Chai Wah Wu_, Sep 11 2019
%Y A063095 Cf. A005250, A001223, A063096.
%K A063095 nonn
%O A063095 1,2
%A A063095 _Labos Elemer_, Aug 07 2001