A244280 Denominators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + ...).

2, 2, 11, 27, 202, 870, 8129, 50681, 570638, 4673558, 61724211, 627102091, 9514420518, 115483788186, 1980202320561, 27962630844865, 534877446987082, 8615820301234778, 181912525664114699, 3292162161484924619, 76056192127792619858, 1527880958525256735838

Offset: 1

Author

Mohamed Sabba, Jun 24 2014

Keywords

• nonn
• frac

Comments

As n-->inf, a(n) converges to 0.628736607098954801603428...

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.

Examples

			a(1) = 1/(1+1) = 1/2;
a(2) = 1/(1+1/(2-1)) = 1/2;
a(3) = 1/(1+1/(2-1/(3+1))) = 7/11;
a(4) = 1/(1+1/(2-1/(3+1/(4-1)))) = 17/27.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A244279 (Numerators).

Programs

Maple

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

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)
vector(30, n, a(n)) \\ Colin Barker, Jul 20 2014

Extensions

More terms from Colin Barker, Jul 20 2014