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
Keywords
Examples
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.
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
Programs
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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} -
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