Thread: visualizing prime families View Single Post
2011-04-22, 20:05   #6
Wini

Apr 2011
 Originally Posted by Batalov Most tables don't bother with odd number sequences, but you can generate your own simple table by pari/gp> for (n=2,10000000,write("mytable1",n," ",sigma(n)-n)) and then analyze the output for cycles, multiple entries into a node etc... After the sequence which ends with 6 was found, I played with this idea for a while. There are some bottlenecks in some descents, and some others are highly branched. Note: 28 is unreacheable (except from itself); it is a singleton. 6 and 496 have an entry and a cycle into itself... etc etc etc. Some highly branched nodes are Code: 129 2731 127 2941 117 2971 116 2521 115 2311 115 2851 113 2881 111 2641 109 2761 ...(there are undoubtedly nodes with more entries)... This is similar to EndGame TableBases. Incidentally, the OEIS sequence A048138 will describe the number of entries into a node n (offset of this sequence is 2). For visualization, you may want to try something like Cytoscape.