A118824 - OEIS

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A118824

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

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

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OFFSET

1,1

COMMENTS

Limit of convergents equals zero; only the 6th convergent is indeterminate. Other 2-adic continued fractions of zero are: A118821, A118827, A118830. 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 A118825(k)/A118826(k):

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

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

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

at k = 4*n-1: 0.

Convergents begin:

-2/1, -1/1, 0/-1, -1/-1, 2/1, 1/0, 0/1, 1/4,

-2/-7, -1/-3, 0/-1, -1/-5, 2/9, 1/4, 0/1, 1/12,

-2/-23, -1/-11, 0/-1, -1/-13, 2/25, 1/12, 0/1, 1/16,