A112768 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

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}]

PROG