A071867 Maximum element in the continued fraction for prime(n+1)/prime(n).

2, 2, 2, 3, 5, 4, 8, 4, 5, 14, 6, 9, 20, 10, 7, 8, 29, 10, 16, 35, 12, 19, 13, 11, 24, 50, 25, 53, 27, 14, 31, 21, 68, 13, 74, 25, 26, 40, 27, 28, 89, 18, 95, 48, 98, 16, 17, 55, 113, 57, 38, 119, 24, 41, 42, 43, 134, 45, 69, 140, 28, 20, 76, 155, 78, 22, 55, 33, 173, 87, 58

Offset: 1

Author

Benoit Cloitre, Jun 09 2002

Keywords

• easy
• nonn

Examples

			prime(5)/prime(4) = 11/7, the continued fraction of 11/7 is [1, 1, 1, 3], hence a(4) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071866.

Programs

Mathematica

Table[Max[ContinuedFraction[Prime[n+1]/Prime[n]]],{n,80}] (* Harvey P. Dale, Dec 24 2015 *)

PARI

for(n=1,200,print1(vecmax(contfrac(prime(n+1)/prime(n))),","))