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 A244280 #27 Mar 21 2020 09:41:16 %S A244280 2,2,11,27,202,870,8129,50681,570638,4673558,61724211,627102091, %T A244280 9514420518,115483788186,1980202320561,27962630844865,534877446987082, %U A244280 8615820301234778,181912525664114699,3292162161484924619,76056192127792619858,1527880958525256735838 %N A244280 Denominators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + ...). %C A244280 As n-->inf, a(n) converges to 0.628736607098954801603428... %C A244280 This is the result of taking the denominator of a continued fraction with alternating signs a(n) = 1/(1+1/(2-1/(3+1/(4-...1/(n +/- 1))))), where addition follows an odd number and subtraction follows an even number. %H A244280 Robert Israel, <a href="/A244280/b244280.txt">Table of n, a(n) for n = 1..449</a> %e A244280 a(1) = 1/(1+1) = 1/2; %e A244280 a(2) = 1/(1+1/(2-1)) = 1/2; %e A244280 a(3) = 1/(1+1/(2-1/(3+1))) = 7/11; %e A244280 a(4) = 1/(1+1/(2-1/(3+1/(4-1)))) = 17/27. %p A244280 seq(denom(numtheory:-cfrac([0, [1,1], seq([(-1)^j,j],j=2..n),[(-1)^(n+1),1]])), n = 1..40); # _Robert Israel_, Jan 17 2016 %o A244280 (PARI) a(n) = if(n%2==0,s=-1,s=1); t=1; while(n>0, t=n+s/t; n--; s=-s); denominator(t=1/t) %o A244280 vector(30, n, a(n)) \\ _Colin Barker_, Jul 20 2014 %Y A244280 Cf. A244279 (Numerators). %K A244280 nonn,frac %O A244280 1,1 %A A244280 _Mohamed Sabba_, Jun 24 2014 %E A244280 More terms from _Colin Barker_, Jul 20 2014