A118830 - OEIS

A118830

2-adic continued fraction of zero, where a(n) = -1 if n is odd, 2*A006519(n/2) otherwise.

-1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 32, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 64, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 16, -1, 2, -1, 4, -1, 2, -1, 8, -1, 2, -1, 4, -1, 2, -1, 32, -1, 2, -1

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OFFSET

1,2

COMMENTS

Limit of convergents equals zero; only the 6th convergent is indeterminate. Other 2-adic continued fractions of zero are: A118821, A118824, A118827. A006519(n) is the highest power of 2 dividing n; A080277 = partial sums of A038712, where A038712(n) = 2*A006519(n) - 1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

For n >= 1, convergents A118831(k)/A118832(k):

at k = 4*n: 1/(2*A080277(n));

at k = 4*n+1: 1/(2*A080277(n)-1);

at k = 4*n+2: 1/(2*A080277(n)-2);

at k = 4*n-1: 0.

Convergents begin:

-1/1, -1/2, 0/-1, -1/-2, 1/1, 1/0, 0/1, 1/8,

-1/-7, -1/-6, 0/-1, -1/-10, 1/9, 1/8, 0/1, 1/24,

-1/-23, -1/-22, 0/-1, -1/-26, 1/25, 1/24, 0/1, 1/32,