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MRB constant T

Marvin Ray Burns 550 Maple
January 13 2012
0


Let c=MRB constant -1/2

Digits := 100; -1; c := evalf(sum((-1)^n*n^(1/n), n = 1 .. infinity))

-.3121403575379328797514820659457267699440969050998612138279953159105227684353397862967033455668925031

 (1)

 

Then look at the repeated power towers of c. The results are periodic with a period of 5  (Incuded in the repeated powers are 0 and 1!)

``

c^c

.8003984393317765330875848879899786583741739167216404052035567506700795231958978778623251934482880613-1.194955986108684540697285841005204929051356404169396850627804054413936260726107544488774888949848882*I

 (2)

c^(c^c)

-12.13772455597847457469272887318061402634917053279865846943075374798270674218595109624334081115845962-11.63427896407485096042195143155929654844011538783728034161408034980373495684700084576272970826984570*I

 (3)

c^(c^(c^c))

8760713499692577233130.145497906970201344959107055647121374638371731700803279842347554955211375197999+5332418260850895293684.119293902652482387156020206456434111364342119614073681251839011004534402684802*I

 (4)

c^(c^(c^(c^c)))

0.+0.*I

 (5)

c^(c^(c^(c^(c^c))))

1.+0.*I

 (6)

c^(c^(c^(c^(c^(c^c)))))

-.3121403575379328797514820659457267699440969050998612138279953159105227684353397862967033455668925031+0.*I

 (7)

Compare those results with a neighboring number: Here we also have a period of 5, but we doln't have 0 and 1.

d := -.45000000000000000000000000000000000000000000000000000000000000000000000000000000000000

-.45000000000000000000000000000000000000000000000000000000000000000000000000000000000000

 (8)

d^d

.2240715973565248496309818194049563460299962073497484010446449886209630431258989058826344754548154868-1.414732387205415152609061066462209520721993440513384283566243897977490475700549479634168621198941395*I

 (9)

d^(d^d)

-18.49989917624910876169865533098838084883100117139246518088162466790628257272368480508633870852463861+68.76175485110781285163966764373670516595481900296876662633500910710997947335173204675372635700172973*I

 (10)

d^(d^(d^d))

0.3958341721440161503629538706541317960205394276355849619708818058783346007736756686496253545140922478e-87+0.2830978239214559317911513246885387694923399677222283781223727582652500265224500444640137945672671661e-88*I

 (11)

d^(d^(d^(d^d)))

.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999995949855627291+0.1220944148129060101162049920935627891109412071194616310984026242076224655460439375641069170061445034e-86*I

 (12)

d^(d^(d^(d^(d^d))))

-.4499999999999999999999999999999999999999999999999999999999999999999999999999999999999984194640905655+0.1011295655847526071638930977037991192230074297762004276411733657816502852627846215872330945526064253e-86*I

 (13)

d^(d^(d^(d^(d^(d^d)))))

.2240715973565248496309818194049563460299962073497484010446449886209630431258989058826393630446698981-1.414732387205415152609061066462209520721993440513384283566243897977490475700549479634161409329787454*I

 (14)

d^(d^(d^(d^(d^(d^(d^d))))))

-18.49989917624910876169865533098838084883100117139246518088162466790628257272368480508650720336833784+68.76175485110781285163966764373670516595481900296876662633500910710997947335173204675172255031165020*I

 (15)

``

``

Compare with another neighboring number, however, and we do have the 0 and 1:.

d := -.31000000000000000000000000000000000000000000000000000000000000000000000000000000000000

-.31000000000000000000000000000000000000000000000000000000000000000000000000000000000000

 (16)

d^d

.8081251396414595057707132895939224681870221069421633345167334571704874392582937673041527456378242608-1.189120032573180381365918011809476334712521739117926001735410468877214640330715885446162821018254831*I

 (17)

d^(d^d)

-11.45227316721805881338585488778584052786752584639832920870732328082542099134070087153237324649405150-11.55549429727114467493508424970253619463846987447864760518228206942293967998433305561881929697396620*I

 (18)

d^(d^(d^d))

-3505912360610848572951.735305977723292050105157152887579190184549218002762047745448966029368872578572+1709274227766564700586.139898277136557526427594421932054246567692145133757274321688717750162058065159*I

 (19)

d^(d^(d^(d^d)))

0.+0.*I

 (20)

d^(d^(d^(d^(d^d))))

1.+0.*I

 (21)

d^(d^(d^(d^(d^(d^d)))))

-.31000000000000000000000000000000000000000000000000000000000000000000000000000000000000+0.*I

 (22)

d^(d^(d^(d^(d^(d^(d^d))))))

.8081251396414595057707132895939224681870221069421633345167334571704874392582937673041527456378242608-1.189120032573180381365918011809476334712521739117926001735410468877214640330715885446162821018254831*I

 (23)

NULL

NULL

NULL

``


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