Math::NumSeq::SternDiatomic -- Stern's diatomic sequence
use Math::NumSeq::SternDiatomic; my $seq = Math::NumSeq::SternDiatomic->new; my ($i, $value) = $seq->next;
This is Moritz Stern's diatomic sequence
0, 1, 1, 2, 1, 3, 2, 3, ...
It's constructed by successive levels as D(2*i)=D(i) and D(2*i+1)=D(i)+D(i+1), so effectively the sequence is extended by interleaving the previous level with sums of adjacent terms,
0, i=0 1, i=1 1, 2, i=2,3 1, 3, 2, 3, i=4,5,6,7 1,4,3,5,2,5,3,4, i=8,9,...,15
For example the i=4 row is a copy of the preceding 1,2 with sums 1+2 and 2+1 interleaved. The new entry at the end of each row is the sum of the last of the previous row and the first of the current row (which is always 1).
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$value = $seq->ith($i)
$i'th value of the sequence.
$bool = $seq->pred($value)
Return true if
$valueoccurs in the sequence, which means simply integer
Copyright 2011, 2012 Kevin Ryde
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