login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244279 Numerators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + ...). 4
1, 1, 7, 17, 127, 547, 5111, 31865, 358781, 2938437, 38808271, 394282041, 5982064475, 72608885159, 1245025688399, 17581129642961, 336297031232409, 5417081623572649, 114375064174857015, 2069902867431592833, 47819312187294567447, 960634689914268797707 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

As n-->inf, a(n)/A244280(n) converges to 0.628736607098954801603428... ; this number has a surprisingly elegant standard continued fraction representation of [0; 1, 1, 1, 2, 3, 1, 4, 5, 1, 6, 7, 1, 8, 9...].

LINKS

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

FORMULA

This is the result of taking the numerator 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.

EXAMPLE

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.

MAPLE

seq(numer(numtheory:-cfrac([0, [1, 1], seq([(-1)^j, j], j=2..n), [(-1)^(n+1), 1]])), n = 1..40); # Robert Israel, Jan 17 2016

PROG

(PARI) a(n) = if(n%2==0, s=-1, s=1); t=1; while(n>0, t=n+s/t; n--; s=-s); numerator(t=1/t)

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

CROSSREFS

Cf. A244280 (Denominators).

Sequence in context: A266382 A118108 A227506 * A325584 A214149 A147643

Adjacent sequences:  A244276 A244277 A244278 * A244280 A244281 A244282

KEYWORD

nonn,frac

AUTHOR

Mohamed Sabba, Jun 24 2014

EXTENSIONS

More terms from Colin Barker, Jul 20 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 4 15:36 EST 2020. Contains 338928 sequences. (Running on oeis4.)