A112768 Sum of terms of continued fraction for prime(n+1)/prime(n).

3, 4, 5, 6, 8, 8, 11, 9, 10, 17, 12, 14, 23, 15, 14, 15, 32, 17, 21, 38, 19, 24, 20, 20, 29, 53, 30, 56, 32, 23, 36, 28, 71, 24, 77, 32, 33, 45, 34, 35, 92, 29, 98, 53, 101, 23, 24, 60, 116, 62, 45, 122, 35, 48, 49, 50, 137, 52, 74, 143, 35, 35, 81, 158, 83, 30, 62, 40, 176

Offset: 1

Author

Ray Chandler, Sep 18 2005

Keywords

• nonn
• look

Examples

			Prime(6)/prime(5) = 13/11 = 1 + 1/(5 + 1/2), so a(5) = 1+5+2 = 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071866, A110021, A109374, A112323, A112324.

Programs

Maple

seq(convert(numtheory:-cfrac(ithprime(n+1)/ithprime(n), quotients),`+`),n=1..100); # Robert Israel, Jul 11 2017

Mathematica

Table[Plus @@ ContinuedFraction[Prime[n + 1]/Prime[n]], {n, 70}]

PARI

a(n) = vecsum(contfrac(prime(n+1)/prime(n))); \\ Michel Marcus, Jul 12 2017