A112323 a(n) = numerator of sum of reciprocals of the terms of the continued fraction for prime(n+1)/prime(n).

3, 5, 2, 10, 17, 19, 13, 31, 38, 11, 41, 49, 31, 73, 82, 93, 89, 19, 115, 107, 5, 136, 148, 107, 31, 38, 178, 161, 139, 67, 220, 236, 103, 256, 56, 181, 47, 283, 302, 313, 269, 52, 287, 61, 74, 65, 69, 388, 341, 289, 423, 359, 137, 456, 467, 478, 101, 107, 349, 211

Offset: 1

Author

Leroy Quet, Sep 03 2005

Keywords

• nonn
• frac

Examples

			prime(6)/prime(5) = 13/11 = 1 + 1/(5 + 1/2).
So a(5) is 17, the numerator of 17/10 = 1 + 1/5 + 1/2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A071866, A110021, A109374, A112324, A112768.

Programs

Mathematica

f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Prime[n + 1]/Prime[n]]; Table[Numerator[f[n]], {n, 60}] (* Ray Chandler, Sep 07 2005 *)

Extensions

Extended by Ray Chandler, Sep 07 2005