[seqfan] Re: paperfolding and continued fraction expansion

Joerg Arndt arndt at jjj.de
Fri May 7 19:07:20 CEST 2010

* Dimitri Hendriks <diem at cs.vu.nl> [May 07. 2010 15:20]:
> [...]
> Then about a possible contribution linking sequences A014577 and
> A088431 (and so A007400): I experimentally found (no proof yet) that
> the sequence of run lengths of the regular paperfolding sequence
> (A014577) is related to A007400, the continued fraction expansion of
> the sum of the series 1/2,1/4,1/16,1/256,... . Namely it is sequence
> A088431, which is the tail^2 of A007400 with the values halved.

The following papers may be useful (URLs may be preprints):

Alfred J.\ van der Poorten, J.\ Shallit: {Folded Continued Fractions},
Journal of Number Theory, vol.40, no.2, pp.237-250, (February-1992)

Jean-Paul Allouche, Anna Lubiw, Michel Mend\'{e}s France,
Alfred J.\ van der Poorten, Jeffrey Shallit:
{Convergents of folded continued fractions},
Acta Arithmetica, vol.77, pp.77-96, (1996).
URL: \url{http://www.lri.fr/~allouche/bibliorecente.html}

> [...]

best regards,   jj

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