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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1285.0. "Somos Sequence" by NOEDGE::HERMAN (Franklin B. Herman DTN 291-0170 PDM1-1/J9) Fri Aug 10 1990 12:24

	The following recurrance relation / divisability sequence, 
    appropriately called the "Somos Sequence", was discovered a few 
    years ago by my good friend Michael Somos of Cleveland, Ohio.

	Define 

	    a[0] = ... = a[5] = 1,

		and for n >= 6

	    a[n] = (a[n-1]*a[n-5]+a[n-2]*a[n-4]+a[n-3]*a[n-3])/a[n-6] 

	Show that a[n] is an integer for all n.

    -Franklin
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1285.1TRACE::GILBERTOwnership ObligatesFri Aug 10 1990 15:5634
The first few numbers are (a[10]=75) :

1, 1, 1, 1, 1, 1, 3, 5, 9, 23,
75,
421,
1103,
5047,
41783,
281527,
2534423,
14161887,
232663909,
3988834875,
45788778247,
805144998681,
14980361322965,
620933643034787,
16379818848380849,
369622905371172929,
20278641689337631649,
995586066665500470689,
72559962302147228286849,
3168992022738213982117009,
221854781474421326332728867,
34951475856493152962631211765,
3005008339620413915704574809401,
379699753474675720531626584024807,
42606783751977661765276440842589595,
10020113764332067086831900975461477669,
2805544254961009286582550261484547842687,
402004673245137783457597234268511135937943,
123986002848096487052630935704945650126513527,
45251164322973497752396978480914726081428497143,
22599166259222085350659654748156962100247034494647
1285.2GUESS::DERAMODan D'EramoFri Aug 10 1990 17:344
	So what is the name of the curve swept out by the
	base ten representations in .-1? :-) :-)

	Dan
1285.3first cut at itHERON::BUCHANANcombinatorial bomb squadTue Aug 14 1990 17:0863
1285.4more thoughtsHERON::BUCHANANcombinatorial bomb squadWed Aug 15 1990 16:0245