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
Jinyuan Wang, Table of n, a(n) for n = 1..448
EXAMPLE
(1-1/(2+1)) = 2/3, so a(1) = 3;
(1-1/(2+1/(3-1))) = 3/5, so a(2) = 5;
(1-1/(2+1/(3-1/(4+1)))) = 19/33, so a(3) = 33;
(1-1/(2+1/(3-1/(4+1/(5-1))))) = 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)
vector(30, n, a(n)) \\ corrected by Mohammed Sabba, Dec 22 2015
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Mohamed Sabba, Nov 20 2015
EXTENSIONS
More terms from Mohamed Sabba, Dec 22 2015
STATUS
approved