Math::NumSeq::BaumSweet -- Baum-Sweet sequence
use Math::NumSeq::BaumSweet; my $seq = Math::NumSeq::BaumSweet->new; my ($i, $value) = $seq->next;
The Baum-Sweet sequence
1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, ... starting i=0
where each value is 1 if the index i written in binary contains no odd-length run of 0-bits, or 0 if it does.
Leonard E. Baum and Melvin M. Sweet, "Continued Fractions of Algebraic Power Series in Characteristic 2", Annals of Mathematics, volume 103, number 3, May 1976, pages 593-610. "/www.jstor.org/stable/1970953" in href="http:
This sequence is the coefficients of a Laurent series which is the unique solution to
f(x)^3 + (1/x)*f(x) + 1 = 0
and which they note has the bitwise interpretation above. Their interest was in certain continued fractions forms for the series.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$value = $seq->ith($i)
$i'th BaumSweet number, ie. 1 or 0 according to whether
$iis without or with an odd-length run of 0-bits.
$bool = $seq->pred($value)
Return true if
$valueoccurs in the sequence, which simply means 0 or 1.
Copyright 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 Kevin Ryde
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