A063095 Record prime gap among first n+1 primes.

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).)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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

Cf. A005250, A001223, A063096.

Sequence in context: A164717 A164715 A164632 * A156726 A082852 A083551

Adjacent sequences: A063092 A063093 A063094 * A063096 A063097 A063098

Keyword

nonn

Author

Labos Elemer, Aug 07 2001

Status

approved