A161794 Largest prime gap for primes less than (n+1)^2.

1, 2, 4, 4, 6, 6, 6, 6, 8, 8, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 18, 18, 18, 18, 18, 18, 18, 20, 20, 20, 22, 22, 22, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34

Offset: 1

Author

Daniel Tisdale, Jun 19 2009

Keywords

• nonn

Examples

			For n = 1, the primes less than (n+1)^2 = 4 are 2,3. The only prime gap is 3 - 2 = 1, and this is the first element in the sequence.
For n = 2, the primes less than 9 are 2,3,5,7. The prime gaps are {1, 2,2}, of which the largest is 2. This is the second element in the sequence.
		

Crossrefs

Cf. A001223, A005250.

Programs

PARI

a(n) = my(vp = primes(primepi((n+1)^2))); vecmax(vector(#vp-1, k, vp[k+1] - vp[k])); \\ Michel Marcus, Aug 15 2022

Extensions

Edited and extended by Ray Chandler, May 06 2010