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A063095
Record prime gap among first n+1 primes.
5
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, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14
OFFSET
1,2
REFERENCES
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).)
EXAMPLE
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.
MATHEMATICA
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}
PROG
(Python)
from sympy import nextprime
def A063095(n):
c, p = 0, 2
for i in range(n):
q = nextprime(p)
c, p = max(c, q-p), q
return c # Chai Wah Wu, Sep 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 07 2001
STATUS
approved