# Converting $\pi$ to senary base

We are decorating the ginger bread house and want to write out $\pi$ on the roof. We have candy with $6$ different colors so we want to use the senary number as the base. What would $\pi$ be with $44$ digits in the senary number base?

We decided to arrange the colors of the candy after their wavelenght. Since we figured out that our brown color is not on the colorspectrume we decided to drop it. So we now need to know $\pi$ in the base 5. Thanks for all the help and sorry for changing the question. We still need 44 digits.

Here is a picture of the finished house.

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Sweet! :-) $\;$ – Brian M. Scott Nov 30 '12 at 21:17
Why $\pi$? Wouldn't logs be better for the roof? – copper.hat Nov 30 '12 at 21:24
How about changing it to use 6 being related to the Mersenne prime 3, since 2^1(2^2 - 1) = 6? See also: mysticalnumbers.com/number-6 for other ideas. :-) – Amzoti Nov 30 '12 at 21:34
We ended up using brown as the decimal point to make it harder to understand. – Anders Nov 30 '12 at 22:14
@copper.hat: $\pi$ because it's edible. – TonyK Nov 30 '12 at 22:20

According to this site,

$$\pi\approx 3.03232 21430 33432 41124 12240 41402 31421 11430 20310_{\text{five}}\;,$$

and

$$\pi\approx 3.05033 00514 15124 10523 44140 53125 32110 23012 14442_{\text{six}}\;,$$

where in each case I’ve kept $45$ places to the right of the point.

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Alpha gives $3.050330051415124105234414053125321102301214442004115252553\\31420333131135535131233455334100151543444012343544520300450024223431..._6$

or

$3.03232214303343241124122404140231421114302031002200344413221101\\04033213440043244401441042334133011323123421042011132102114201..._5$

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Did not know you could use wolfram to do that. Smart! – Anders Nov 30 '12 at 22:13

EDIT: D'oh, you ate up all the brown sweets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

For a really swet surprise, consider $$3_60503300514151241052344140531253211023012144420\\ 04115252553314203331311355351312334553341001515\\ 43444012343544520300450024223431402513114521100\\ 20251031010503410355135533050550325533003214415\\ 23154243140500010113054135235552155133504313345\\ 22214530520215100514204341303313333102104445052\\ 01223531244053341442311411410310515402520324103\\ 25122254530424321134551440542544301335053210342\\ 11521112514550413013341021055121432143035114223\\ 55101504135255400410333550122402040012005110123\\ 32310341414133002545055004502405541021131311333\\ 12022242140152520000413041101141001350114142411\\ 15503132021301402023322515242431155533510105544\\ 52241015505452542304432104122414423054241210454\\ 34451211510211252031404205415123142240501310242\\ 42010135054431332322520421445252442040241040353\\ 35315045224413020512350334344015320332032030431\\ 30040320322002314155333325231413100411552444002\\ 03122530542543021203142135102541112302034044113\\ 04333223212345211552213540540011152211105140015\\ 35102131503125032401503214005244000513325115510\\ 30033535412254243555145252231232553112340535244\\ 43154353020241021353405421232250233203030050044\\ 21431405053003250514351430120305150000521533114\\ 32303434105430234211104525145540415101452551444\\ 24430555414432345334041523345413022054042235332\\ 40055024043451204235301153324352321153001102254\\ 02330445531535211531542330543012305020403355444\\ 32413525502233400350134240340415350221554532155\\ 54425201005340555341525244340425103300012100141\\ 30332352421241204402025241403252422154535212515\\ 10041302114011502520335545313112512433032234321\\ 15123335343255110503014454524540023435025041043\\ 22230103511520201223340003240403424330452140054\\ 53303100413200104245052221425310533340225522302\\ 00133051425132054101200425245400223351520324435\\ 35203333104231023311222101505032011122435254441\\ 14203223253013355054120444424030050310040511520\\ 31301435251452214104120210551515502105541554042\\ 30524413425103551202323215503510015240000530045\\ 44425321553430121240310004220003515545535313231\\ 51224554151515224030115350412315211010034341453\\ 03032041342213530144433244$$

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How does considering that string of numbers make anything sweeter?? – The Chaz 2.0 Nov 30 '12 at 22:15
@TheChaz More digits, more sweets. ;) – Hagen von Eitzen Nov 30 '12 at 23:45