

A263295


Denominators of the nth iteration of the alternating continued fraction formed from the positive integers, starting with (1  ...).


3



3, 5, 33, 111, 933, 4913, 50585, 364717, 4460647, 40920133, 580574377, 6472209467, 104581586665, 1373040648769, 24902871413201, 376386726269561, 7573128424949291, 129519388933667493, 2863373356440803473, 54670305859684290279, 1317404009250178503245
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OFFSET

1,1


COMMENTS

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, ...].


LINKS



EXAMPLE

(11/(2+1)) = 2/3, so a(1) = 3;
(11/(2+1/(31))) = 3/5, so a(2) = 5;
(11/(2+1/(31/(4+1)))) = 19/33, so a(3) = 33;
(11/(2+1/(31/(4+1/(51))))) = 64/111, so a(4) = 111.


PROG

(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)


CROSSREFS

Same principle as A244279 and A244280  except here we begin with subtraction rather than addition.


KEYWORD

nonn,frac


AUTHOR



EXTENSIONS



STATUS

approved



