This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071866 #20 Aug 10 2025 02:57:08
%S A071866 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 A071866 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 A071866 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 A071866 Number of elements in the continued fraction for prime(n+1)/prime(n).
%H A071866 Robert Israel, <a href="/A071866/b071866.txt">Table of n, a(n) for n = 1..10000</a>
%e A071866 prime(5)/prime(4) = 11/7, 11/7 continued fraction is [1, 1, 1, 3] which contains 4 elements, hence a(4)=4.
%p A071866 seq(nops(convert(ithprime(n+1)/ithprime(n),confrac)),n=1..200); # _Robert Israel_, May 29 2018
%t A071866 Table[Length[ContinuedFraction[Prime[n + 1]/Prime[n]]], {n, 105}] (* _Ray Chandler_, Sep 18 2005 *)
%o A071866 (PARI) a(n) = length(contfrac(prime(n+1)/prime(n)));
%Y A071866 Cf. A110021, A109374, A112323, A112324, A112768.
%K A071866 easy,nonn
%O A071866 1,1
%A A071866 _Benoit Cloitre_, Jun 09 2002
%E A071866 More terms from _Hans Havermann_, Jul 06 2002