A071866 - OEIS

%I #14 May 29 2018 21:40:16

%S 2,3,3,4,3,3,3,4,4,3,3,3,3,4,4,4,3,3,4,3,3,4,4,3,3,3,4,3,3,3,4,4,3,4,

%T 3,3,3,4,4,4,3,3,3,3,3,6,6,4,3,3,4,3,3,4,4,4,3,3,3,3,4,4,4,3,3,6,3,5,

%U 3,3,4,4,3,3,4,4,6,3,3,4,3,3,3,3,4,4,3,3,3,4,4,4,4,5,4,4,5,3,3,3,5,4,4,3,3

%N Number of elements in the continued fraction for prime(n+1)/prime(n).

%H Robert Israel, <a href="/A071866/b071866.txt">Table of n, a(n) for n = 1..10000</a>

%e prime(5)/prime(4) = 11/7, 11/7 continued fraction is [1, 1, 1, 3] which contains 4 elements, hence a(4)=4.

%p seq(nops(convert(ithprime(n+1)/ithprime(n),confrac)),n=1..200); # _Robert Israel_, May 29 2018

%t Table[Length[ContinuedFraction[Prime[n + 1]/Prime[n]]], {n, 105}] - _Ray Chandler_, Sep 18 2005

%o (PARI) for(n=1,200,print1(length(contfrac(prime(n+1)/prime(n))),","))

%Y Cf. A110021, A109374, A112323, A112324, A112768.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Jun 09 2002

%E More terms from _Hans Havermann_, Jul 06 2002