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 |
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
T.R | Title | User | Personal Name | Date | Lines |
---|---|---|---|---|---|
1285.1 | TRACE::GILBERT | Ownership Obligates | Fri Aug 10 1990 15:56 | 34 | |
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 | |||||
1285.2 | GUESS::DERAMO | Dan D'Eramo | Fri Aug 10 1990 17:34 | 4 | |
So what is the name of the curve swept out by the base ten representations in .-1? :-) :-) Dan | |||||
1285.3 | first cut at it | HERON::BUCHANAN | combinatorial bomb squad | Tue Aug 14 1990 17:08 | 63 |
1285.4 | more thoughts | HERON::BUCHANAN | combinatorial bomb squad | Wed Aug 15 1990 16:02 | 45 |