A063095 - OEIS

%I #12 Sep 11 2019 16:37:12

%S 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 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,

%U 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 Record prime gap among first n+1 primes.

%D 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 Chai Wah Wu, <a href="/A063095/b063095.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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 (Python)

%o from sympy import nextprime

%o def A063095(n):

%o     c, p = 0, 2

%o     for i in range(n):

%o         q = nextprime(p)

%o         c, p = max(c,q-p), q

%o     return c # _Chai Wah Wu_, Sep 11 2019

%Y Cf. A005250, A001223, A063096.

%K nonn

%O 1,2

%A _Labos Elemer_, Aug 07 2001