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 A263295 #33 Jul 25 2021 07:02:00 %S A263295 3,5,33,111,933,4913,50585,364717,4460647,40920133,580574377, %T A263295 6472209467,104581586665,1373040648769,24902871413201,376386726269561, %U A263295 7573128424949291,129519388933667493,2863373356440803473,54670305859684290279,1317404009250178503245 %N A263295 Denominators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - ...). %C A263295 As n->inf, A262957(n)/a(n) converges to 0.57663338973018...; this number has a surprisingly elegant standard continued fraction representation: [0; 1, 1, 2, 1, 3, 4, 1, 5, 6, 1, 7, 8, ...]. %H A263295 Jinyuan Wang, <a href="/A263295/b263295.txt">Table of n, a(n) for n = 1..448</a> %e A263295 (1-1/(2+1)) = 2/3, so a(1) = 3; %e A263295 (1-1/(2+1/(3-1))) = 3/5, so a(2) = 5; %e A263295 (1-1/(2+1/(3-1/(4+1)))) = 19/33, so a(3) = 33; %e A263295 (1-1/(2+1/(3-1/(4+1/(5-1))))) = 64/111, so a(4) = 111. %o A263295 (PARI) a(n) = if(n%2==0, s=-1, s=1); t=1; while(n>0, t=n+1+s/t; n--; s=-s); denominator(t=1/t) %o A263295 vector(30, n, a(n)) \\ corrected by _Mohammed Sabba_, Dec 22 2015 %Y A263295 Same principle as A244279 and A244280 - except here we begin with subtraction rather than addition. %Y A263295 Cf. A262957 (numerators). %K A263295 nonn,frac %O A263295 1,1 %A A263295 _Mohamed Sabba_, Nov 20 2015 %E A263295 More terms from _Mohamed Sabba_, Dec 22 2015