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THE SUMMED PAPERFOLDING SEQUENCE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 110 / Issue 2 / October 2024
- Published online by Cambridge University Press:
- 25 March 2024, pp. 189-198
- Print publication:
- October 2024
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- Article
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The sequence
$a( 1) ,a( 2) ,a( 3) ,\ldots, $ labelled A088431 in the Online Encyclopedia of Integer Sequences, is defined by: 
$a( n) $ is half of the 
$( n+1) $th component, that is, the 
$( n+2) $th term, of the continued fraction expansion of 
$$ \begin{align*} \sum_{k=0}^{\infty }\frac{1}{2^{2^{k}}}. \end{align*} $$Dimitri Hendriks has suggested that it is the sequence of run lengths of the paperfolding sequence, A014577. This paper proves several results for this summed paperfolding sequence and confirms Hendriks’s conjecture.
