Initial data commit

Task/Partition-function-P/Factor/partition-function-p.factor

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+USING: kernel lists lists.lazy math sequences sequences.extras ;
+
+! Compute the nth pentagonal number.
+: penta ( n -- m ) [ sq 3 * ] [ - 2/ ] bi ;
+
+! An infinite lazy list of indices to add and subtract in the
+! sequence of partitions to find the next P.
+: seq ( -- list )
+    1 lfrom [ penta 1 - ] <lazy-map> 1 lfrom [ neg penta 1 - ]
+    <lazy-map> lmerge ;
+
+! Reduce a sequence by adding two, subtracting two, adding two,
+! etc...
+: ++-- ( seq -- n ) 0 [ 2/ odd? [ - ] [ + ] if ] reduce-index ;
+
+! Find the next member of the partitions sequence.
+: step ( seq pseq -- seq 'pseq )
+    dup length [ < ] curry pick swap take-while over <reversed>
+    nths ++-- suffix! ;
+
+: partitions ( m -- n )
+    [ seq swap [ <= ] curry lwhile list>array ]
+    [ V{ 1 } clone swap [ step ] times last nip ] bi ;