that's the lower ? limit: if so:

[QUOTE]1.048160763796310932532406940721790497083607972712230068811827915593117475301021216847333399205353891[/QUOTE] looks to be the lower limit to put my lowest value >=1.

scratch that:

[CODE](12:42)>for(n=1,#mersenne,print(solve(x=1,20,(mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-x/log(mersenne[n]))-1)))
1.221045211781039641218621908242613887816818178982651231266946543163325501217342917242414949318615982
[COLOR="Red"]1.021017745318224477002391158250826730797295442352557610947905198183666740778662586872855983175813252[/COLOR]
*** roots must be bracketed in solve.[/CODE]

[CODE](12:47)>for(n=1,#mersenne-1,print(solve(x=-10,10,(mersenne[n+1]/mersenne[n])/(n*exp(-Euler)*log(1.78)*1.78^exp(-Euler)^-x/log(mersenne[n]))-1)))
1.221045211781039641218621908242613887816818178982651231266946543163325501217342917242414949318615982
1.021017745318224477002391158250826730797295442352557610947905198183666740778662586872855983175813252
0.6549826526828368183577151707013114476748827930307909955627869130134989722596480676067957138712436359
0.9987908631648755228843447478876116530237200051899251635379003240772227036148421501457988525719941289
0.4052267409168582888557720113896567274771705650312627259856272581089601184003426228756458463566985823
-0.2866708316919592079782584066540847186281803381515177809526170130611131969403186447856222985025989700
0.4585924665831132593559712551865244429861339513204641936987908996902917223088375207974204407982696379
0.8812716462927890695127651513577201383048362176484426831542438569555556586645618538284500589636209338
0.3894820394358417717882636151059958816021887252223221628901103615386542468234250470314224125094088048
-0.2094361779115823418749377454312584518122495166568803485690069767173075374474403785073503083941553317
-0.4565748594144080289308865882770544075881733796602817604897233171891542356582463687506800151766103368
1.802676985070192364236291634996266717393158714633447637842856991558141656783517508496735756415741539
-0.08460929481393289547305879169716849544194692984047134800924735037673752175791358587908620726759709019
1.105822037275535702621814976926679054427928363977232513618245760246767865969614120174322950405157507
0.8302552218662819564095079581592628828735409165696738304701253833034419310308169751230714801063203585
-0.5046186967007588544100286274646138297173416044719733546677081206407616685484030093150766224083933355
0.2954641445452101711602697484953234902580106697707754300431403328674064495406505543316926988014964098
0.08475732322566423726559129084205305683678916097981305339830979320151514558570012428997353114296053901
-0.8875319995143233762444648562162906385319714134823684610953349528065312604856263944006909492086661117
1.028169204353676486599126023019159204530072308358009475702504998702694435767081738473698432575553387
-0.9888062939148641485481861216604714156952458328115130728515631937789640132010533343024139310369132511
-0.7368703356932631210345030086071880547603359848230421721811351802618504119540097659716502610814991835
0.5683329567095742420406774543620266819730021976345398232299142253581679023843733845883850082130306219
-0.9821679292545116769946341777314225358285309606415429976762457359204070183074887668033506749254657242
-1.268904636516073103396990120185290738484991997369220562293511562652723340628743934332271626324966429
0.6276790240689950601167375641820574404430217984981715382984966870980614605703136710711345637484109953
0.7011070092533118566610212108127056572319364017177112306959442850371015195010044341153779254290974620
-0.3394997457980279553008155334939283556397368147517236660770767685747590965853981371631875636560896678
-0.6741435834117947628323563624449849583551324932975127968194894443603014928798985181167684369077619735
0.3020949811101398107195479487370099017075510194248465495780907217102916551504895411862495239334285646
1.604155614927746943000825384834664530528576584626099186809254228263545469673698550461399915901145249
-0.6570965048910669837506915423124464056158817333913983323892160003619129439702112150676220807592471279
0.1448437285612943760361273317280353061877907856078652552830946527897401846633685644682367731379907960
-0.8670062813180255889705213111866279285822129634331884725686760824811247641748921080636726065694112233
0.9146790096275647001143972092585110719899471107438132077369405902123919083845771412748335952529628693
-1.372481449062038178021845005155532039441680318815793705773837636591249887482146733324192978436146724
1.048160763796310932532406940721790497083607972712230068811827915593117475301021216847333399205353891
0.7824151999928314004404512647847017808565429525598779470151978973509417460821627602045802971003505457
0.3521336181631540101393215503335012764245324529017577484906998213110171395661319304476910513927703884[/CODE]

I'm worried what the negatives imply.

when I vecsort v and plot it it looks more solvable from my point of view:

[CODE](13:05)>plot(x=1,#v,v[floor(x)])

1.6041556 |'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''""
| |
| __ |
| _ |
| xxxxx"" |
| __x"" |
| _"" |
| _"""" |
| __xx |
| _xx""" |
| __ |
| "" |
````````````````````````x```````````````````````````````````````
| __xx |
| " |
| xx"" |
| __x |
| "" |
| __""" |
| " |
| |
-1.372481 __""...........................................................|
1 39[/CODE]

[QUOTE=science_man_88;243991]I'm worried what the negatives imply.[/QUOTE]

Those are numbers where the exponent -x is positive. The positive values are where the exponent -x is negative.

[QUOTE=CRGreathouse;243994]Those are numbers where the exponent -x is positive. The positive values are where the exponent -x is negative.[/QUOTE]

is there anyway to make the graph more linear if we can get to linear then it's just a matter of predicting where it falls on that line.

[QUOTE=science_man_88;244006]is there anyway to make the graph more linear if we can get to linear then it's just a matter of predicting where it falls on that line.[/QUOTE]

No, it really wouldn't be.

[QUOTE=CRGreathouse;244010]No, it really wouldn't be.[/QUOTE]

well if we could predict the line and what to check we could use the formula's to convert it to the exponent correct ?

[QUOTE=science_man_88;244019]well if we could predict the line and what to check we could use the formula's to convert it to the exponent correct ?[/QUOTE]

It's the first part, not the second, that gives trouble.

[QUOTE=CRGreathouse;244027]It's the first part, not the second, that gives trouble.[/QUOTE]

what says we can't do something like what we've been doing to get the line, assuming that's the part you mean.

[CODE](13:04)>plot(x=1,#v,v[floor(x)])

1.802677 |''''''''''''''''''"'''''''''''''''''''''''''''''''''''''''''''|
| : xx |
| : :: |
| : :: |
"" : __ :: |
| xx xx : : xx :: "" |
| : xx : : _ :: : : "" : |
| _ : :: :: : : :: _ : : :: : ""
| : : : : : : : :: xx "": : : :: : |
| __ xx _ : :: : :: :: : : : : :: : |
| : : : : :: : xx :: :: : : x : :: : |
| : : : : :: : : _ :: :: : : : : x :: : |
,,,,,,,,,:,,,,,:,,:,::,,,:,:,:,:,,:,,::,,,:,,:,,,:,,:,:,:,:,:,,,
| : __ : "" :: : : : : : : : : : : : :: |
| x : :: : : : : : : __ : ::: : : |
| xx __ :: : : : : : : :: :: : |
| :: : : : : :: __ :: : |
| :: :xx : : "" :: : |
| xx : : : xx : |
| " " : : |
| : : |
-1.372481 |.......................................""................._...|
1 39[/CODE]

Here's the plot of v before organizing it numerically if it helps.