CoCalc Public FilesPossible counter examples to the p-adic Littlewood.sagews
Author: Erez Nesharim
Views : 14
def Dragon(n):
"""
This function returns the nth element of the dragon sequence
"""
if n == 0:
return 0
else:
while Mod(n, 2) == 0:
#while n%2 == 0:
n = n / 2
return ((n-1)/2)%2

def Pagoda(n):
"""
This function returns the nth element of the pagoda sequence
"""
return Dragon(n+1) - Dragon(n-1)

def seqToReal(seq,base=3):
leng = len(seq)
s = 0
oneOverBase = 1/base
for i in range(0,leng):
s += seq[i]*oneOverBase^i
return s

print()
leng = 10000
base = 3
pag = [Pagoda(n) for n in range (0,leng)]
pagBase = [Integer(Mod(pag[n],base)) for n in range (0,leng)]
pagNumber = seqToReal(pagBase,base)
print(pagNumber)
print(pagNumber.continued_fraction())

() 11650752313824165631225243929316685539203128820352252268870982738913140201643801388392645337630473684707566408453628883255554030546974717827947282836132303697751541399450160614792603033354528179834504069812328941834524436357453413771636831129629682610801636882476141906529580020474454941565998038934177164053675002163365775825903800103098423158818672286932356989736589912174096345619859413837738832890853842596615213196398682101818122122554894120942068088738287586653702936616511290015650574486794767511589116958411978790884087801529392928892105402385953998461407625222715306124075822113841720012449537062432007187256695237864114067378374198086723502293967803355402851464241816091952021527832549356314822858194165809624449932414916821847826532494701342610040449096080632112505881824344651535223559835360339087585980716668564078160991688206252840794439079644780659635648988811711658116073114029392389925225849292919199321563609334005416078955267683417714923622936641354342973023596169671047047526070121890752187183733696408282166997359179800757571106671225357757831540404618416310906754900674549538160907455382971702348168130805093478351610502555685268740985274656485891661803624057412116969897548814968614297369146060788618647732823491578096749265658878350178195565126376208211662023258389344140483354510441205639174875211484633156231441049537016537346115448617712906084763697599186307664513708789662028612241498868166423067886935586689834723717736459595436782585552359555518900305881541711256925318505391253382185858911541540525696609279021267447279751816068803084196424121495682824211113119283735209112091164794625575671063929549883126145968128325540545000926170483256926837668902273859125092841021194192229508796285424703896508150122395525940130813987381860012660883716880273924785063059460220248120161694484778683664760885554076016211186627683474210275239624855506810793930256619168535749164874043987602790057263867964781665672533758242152380067518476416411148454322438963821164091952631707194684473221020936046831026290955133669982826538284007097233841643117108969465643925998635325564177918946493391788857521587354616796623356319178874540917528073834962738282131045001642371159374118633782791106105444057403633760791359037119910153602541695092831737320675127605094163962863963413257954333197476791521489169380066305529275209608307806744322143432068571349985590134452580797110459115244016366840045934826002573425526768633134359181895716401484660336898245482022813069538994239961772984118312821676262265209009322589698950862381725913478102264036434973521099884322579496714029145666770625614174202070094380153716333928139562765583067112830815190711732893067692988637171789927219682109728926351089219065935836628702659114856193748433251677530698810085657325171985469915321668964057570689936927030531694689938088223275620094930792816747632438922299356997821139506400998411931511947048739117495774470639279763698861707568865204258643039711784959890757218474001147892843453218532958865612565670153793927298989416908020499943883749916976817360319429228090187811961287733013129473008362268376690604629353895365820773619139232240301869212652907264332402653783613071409130805003335814936436574789856309181037957875097513175715873020804463734432697211704125832312911375719882809690205689997737484524194197483194053525510823209023417848762520685981920315994195861915399273342940869356772279083952286535855916775549170060693838526095565225410341527387890990693949868920031855990314908969136221257866266005070474525843578746824270626838474105752926046480370115576577503078502533772863529188289279050718427877270509227686280445564852402582052685003310415117559909873404643529834327088385273747049370276591586027782339349232459151486797576789895368996755613983490994962242930232361473161197183407818710777086683507122088311855470482742376425662167964973656899845650855574914812023955870264070298424454857229037496365500752147847546005999135256870948245560028607636310678673177080245003304090532375227888308349871111603408545328186420962988816668784937975259085202874573007119081220578611444917811363166386850455267354265782739344490530531648289118006566914591733842639943389299818140927351851671285061745892044545709608508785274057191233577780207125254718576794698743983848611998071236033848358834150341939295768729632994483522797420720476463502084265318952738563089914124384751333324400046736668243654995259465320683112829202118532999260576902825834368327875218273272952842908401843113144298936670265188649028467626625240137803386128281542723976826739175898152027561613442927190870150396595593563807927091939594717155288331389628643633055563396913739743312611336769032664914207782959982433786813158941139171210357995619492476039115930509134372123630069560084898928102774161876396802/54378339511420862476775224306038490560404415119417933131160677539727524360477302624933852102826161032244173484077452651444685276663924012841271597151227041671510641183887414636751412096145188955198865483373380591494251766634577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1, 45, 2, 1, 1, 1, 1, 1, 7, 1, 1, 3, 1, 3, 1, 12, 2, 5, 1, 3, 14, 5, 3, 1, 43, 312, 1, 2, 1, 1, 1, 3, 1, 14, 1, 7, 1, 1, 4, 6, 1, 13, 4, 1, 5, 1, 53, 1, 2, 1, 1, 1, 2, 14, 85, 2, 3, 12, 3, 2, 1, 1, 8, 2, 30, 2, 1, 1, 2, 7, 1, 13, 1, 2, 5, 1, 4, 4, 1, 4, 7, 16, 1, 11, 7, 2, 5, 1, 2, 15, 4, 18, 1, 164, 1, 1, 1, 6, 4, 2, 8, 8, 21, 1, 4, 4, 2, 1, 1, 1, 10, 8, 2, 10, 2, 4, 8, 1, 1, 1, 22, 1, 10, 1, 1, 20, 3, 1, 1, 1, 1, 14, 4, 87, 1, 6, 1, 1, 2, 1, 4, 8, 1, 33, 1, 1, 3, 4, 1, 1, 4, 49, 1, 7, 1, 2, 1, 1, 5, 6, 1, 10, 86, 6, 1, 1, 5, 17, 1, 4, 1, 4, 3, 5, 1, 3, 2, 36, 2, 9, 2, 2, 13, 1, 2, 1, 1, 5, 15, 2, 8, 4021, 1, 13, 6, 3, 3, 1, 1, 2, 2, 23, 2, 1, 3, 53, 1, 1, 1, 45, 5, 2, 2, 2, 1, 6, 3, 6, 2, 1, 4, 2, 2, 10, 1, 7, 2, 1, 2, 109, 4, 2, 1, 4, 18, 1, 1, 10, 7, 5, 5, 9, 1, 7, 1, 4, 1, 2, 2, 2, 3, 6, 4, 5, 1, 1, 2, 4, 1, 2, 3, 3, 2, 5, 1, 2, 1, 51, 2, 1, 5, 1, 3, 3, 3, 1, 1, 3, 1, 1, 1, 1, 1, 2, 6, 1, 4, 2, 1, 1, 1, 3, 7, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 8, 1, 2, 1, 1, 1, 1, 3, 2, 7, 1, 7, 1, 5, 1, 4, 4, 4, 2, 9, 3, 4, 1, 11, 1, 3, 2, 5, 1, 1, 1, 5, 3, 1, 3, 1, 1, 5, 2, 1, 1, 7, 4, 3, 3, 1, 2, 2, 1, 12, 2, 41, 105, 60, 1, 3, 1, 1, 35, 1, 1, 8, 6, 1, 1, 7, 1, 1, 4, 1, 1, 4, 2, 15, 1, 2, 1, 1, 9, 1, 2, 9, 1, 1, 1, 4, 1, 2, 1, 1, 11, 9, 8, 5, 1, 2, 2, 2, 1, 2, 2, 6, 1, 1, 1, 1, 2, 3, 4, 2, 1, 2, 19, 3, 9, 10, 2, 2, 4, 1, 8, 1, 2, 1, 1, 4, 1, 1, 1, 2, 1, 4, 5, 4, 7, 1, 2, 7, 6, 3, 1, 41, 1, 3, 13, 3, 6, 1, 18, 2, 2, 1, 2, 2, 5, 1, 47, 55, 1, 13, 1, 3, 5, 1, 1, 1, 1, 1, 2, 3, 1, 2, 66, 1, 1, 1, 1, 2, 3, 2, 1, 2, 15, 1, 2, 1, 2, 3, 1, 1, 13, 2, 1, 5, 6, 1, 2, 4, 1, 918, 3, 3, 3, 3, 2, 75, 6, 36, 1, 1, 2, 2, 3, 2, 6, 1, 2, 31, 2, 6, 1, 12, 12, 1, 2, 1, 1, 4, 1, 1, 7, 22, 1, 2, 2, 6, 7, 1, 1, 1, 1, 10, 1, 17, 2, 2, 16, 3, 3, 1, 21, 108, 3, 6, 2, 1, 15, 34, 1, 25, 5, 69, 1, 2, 5, 115, 1, 1, 3, 4, 1, 1, 5, 1, 9, 14, 21, 4, 4, 1, 2, 1, 2, 1, 11, 8, 8, 2, 3, 2, 1, 2, 1, 1, 6, 1, 1, 1, 2, 2, 1, 5, 2, 1, 2, 2, 1, 1, 1, 3, 1, 3, 44, 11, 11, 1, 2, 1, 4, 1, 1, 1, 1, 1, 52, 1, 4, 1, 1, 1, 1, 152, 3, 2, 1, 8, 3, 1, 1, 5, 4, 7, 1, 5, 1, 5, 24, 1, 7, 5, 1, 8, 4, 101, 1, 7, 1, 1, 8, 1, 2, 2, 1, 18, 1, 1, 2, 3, 6, 4, 875, 4, 26, 1, 1, 17, 1, 12, 5, 3, 3, 1, 8, 4, 14, 3, 5, 3, 52, 1, 2, 2, 20, 1, 2, 2, 12, 1, 2, 2, 7, 2, 4, 1, 1, 6, 11, 10, 1, 328, 1, 1, 329, 3, 7, 1, 1, 1, 1, 3, 2, 15, 3, 8, 1, 3, 9, 3, 6, 1, 7, 1, 3, 1, 1, 1, 21, 4, 1, 4, 1, 1, 10, 7, 1, 2, 1, 15, 1, 5, 5, 1, 1, 8, 24, 10, 3, 12, 4, 4, 2, 2, 13, 1, 3, 4, 1, 5, 2, 3, 2, 4, 1, 1, 1, 4, 2, 3, 5, 1, 1, 1, 6, 1, 1, 1, 14, 1, 5, 18, 1, 1, 2, 2, 4, 2, 1, 6, 8, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 5, 1, 4, 1, 9, 1, 2, 5, 4, 2, 8, 1, 41, 3, 3, 1, 21, 1, 1, 1, 2, 72, 30, 8, 1, 1, 2, 1, 1, 1, 2, 1, 1, 6, 1, 25, 1, 1, 2, 6, 3, 1, 1, 2, 1, 2, 1, 7, 4, 20, 15, 3, 1, 3, 1, 2, 72, 1, 1, 3, 1, 1, 2, 1, 5, 1, 1, 1, 30, 2, 1, 3, 2, 9, 1, 6, 2, 24, 1, 7, 1, 5, 5, 1, 2, 2, 1, 4, 1, 1, 3, 1, 3, 5, 1, 1, 17, 1, 1, 3, 2, 5, 1, 1, 2, 1, 1, 1, 66, 1, 6, 7, 6, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 3, 3, 3, 1, 5, 7, 2, 2, 36, 2, 1, 21, 5, 1, 1, 4, 1, 5, 3, 9, 1, 1, 2, 4, 1, 2, 6, 2, 5, 1, 1, 3, 1, 2, 43, 45, 12, 18, 12, 349, 2, 1, 5, 1, 2, 1, 1, 1, 30, 4, 1, 6, 24, 2, 26, 1, 2, 1, 2, 1, 1, 1, 1, 111, 2, 43, 2, 4, 2, 1, 2, 1, 9, 2, 4, 4, 1, 87, 1, 8, 1, 2, 3, 5, 1, 106, 4, 3, 1, 7, 2, 1, 3, 4, 2, 1, 6, 2, 1, 1, 5, 2, 1, 1, 1, 1, 35, 2, 1, 2, 1, 1, 3, 20, 17, 2, 3, 1, 1, 2, 10, 5, 1, 1, 5, 1, 2, 21, 56, 1, 1, 1, 9, 6, 2, 1, 1, 1, 134, 4, 4, 3, 11, 2, 3, 1, 5, 3, 1, 1, 1, 1, 2, 7, 1, 1, 3, 1, 3, 8, 1, 31, 4, 2, 8, 11, 4, 2, 17, 1, 1, 2, 1, 2, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2, 6, 2, 37, 1, 16, 6, 1, 17, 1, 1, 2, 1, 1, 7, 4, 3, 1, 1, 3, 2, 1, 2, 1, 1, 5, 1, 1, 5, 1, 2, 2, 13, 3, 2, 1, 9, 1, 1, 97, 1, 17, 59, 1, 1, 1, 1, 8, 3, 1, 1, 6, 2, 2, 1, 1, 7, 1, 10, 1, 1, 1, 6, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 10, 1, 31, 4, 2, 16, 43, 3, 2, 1, 2, 1, 3, 26, 2, 1, 28, 3, 2, 1, 1, 1, 10, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 2, 2, 3, 18, 2, 1, 4, 7, 3, 3, 1, 2, 4, 1, 3, 10, 1, 9, 1, 8, 1, 5, 1, 132, 1, 4, 2, 1, 6, 1, 1, 4, 2, 1, 1, 1, 23, 14, 1, 1, 1, 3, 20, 1, 6, 12, 1, 2, 1, 1, 12, 1, 2, 10, 4, 1, 10, 1, 1, 4, 1, 1, 210, 1, 5, 2, 1, 2, 1, 1, 3, 1, 6, 1, 3, 2, 1, 3, 8, 1, 1, 4, 8, 934, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 14, 2, 1, 5, 4, 5, 1, 9, 3, 1, 14, 1, 1, 5, 11, 3, 1, 13, 1, 1, 4, 1, 1, 6, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 3, 4, 1, 3, 1, 1, 5, 6, 2, 1, 1, 3, 1, 1, 2, 21, 9, 1, 1, 11, 1, 99, 81, 1, 4, 2, 2, 1, 2, 7, 1, 1, 1, 1, 4, 14, 1, 5, 2, 2, 1, 2, 6, 29, 12, 1, 1, 2, 2837, 1, 9, 7, 1, 2, 1, 2, 1, 3, 11, 1, 1, 1, 1, 1, 4, 37, 2, 1, 28, 1, 12, 1, 3, 1, 10, 1, 3, 1, 1, 1, 1, 5, 1, 6, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 4, 1, 4, 2, 2, 1, 62, 4, 10, 2, 1, 27, 1, 2, 7, 1, 2, 12, 1, 1, 5, 3, 1, 1, 18, 2, 1, 2, 2, 4, 2, 1, 2, 1, 1, 1, 2, 9, 13, 10, 1, 3, 2, 1, 42, 2, 4, 1, 5, 1, 5, 1, 1, 5, 9, 11, 4, 5, 3, 3, 4, 1, 1, 17, 1, 19, 2, 2, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 5, 6, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 2, 6, 1, 4, 4, 137, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 22, 48, 1, 1, 1, 149, 3, 57, 1, 1, 11, 3, 5, 2, 1, 6, 1, 4, 9, 3, 18, 1, 2, 1, 5, 2, 1, 7, 2, 47, 1, 2, 23, 11, 1, 2, 2, 22, 3, 81, 1, 1, 2, 11, 2, 76, 1, 3, 4, 1, 1, 1, 2, 4, 1, 79, 1, 1, 1, 10, 1, 1, 2, 1, 2, 2, 2, 18, 14, 3, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 49, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 3, 4, 3, 3, 103, 23, 1, 2, 4, 17, 4, 2, 8, 77, 5, 1, 49, 1, 6, 1, 2, 4, 3, 19, 4, 4, 6, 7, 1, 1, 2, 1, 2, 99, 1, 1, 5, 1, 6, 1, 2, 3, 4, 1, 2, 6, 5, 1, 2, 6, 2, 1, 1, 2, 1, 62, 5, 1, 1, 2, 2, 1, 27, 1, 2, 2, 10, 2, 23, 1, 1, 1, 21, 2, 1, 7, 3, 9, 3, 5, 47, 1, 3, 1, 11, 2, 1, 1, 78, 1, 2, 1, 19, 2, 10, 2, 2, 1, 1, 1, 118, 1, 13, 2, 13, 8, 1, 1, 10, 3, 5, 1, 13, 1, 2, 1, 1, 1, 2, 20, 48, 2, 1, 5, 4, 4, 2, 6, 1, 5, 1, 4, 2, 3, 3, 1, 3, 96, 3, 10, 1, 43, 1, 3, 3, 2, 1, 2, 116, 1, 5, 2, 1, 1, 2, 1, 4, 1, 9, 2, 10, 9, 1, 3, 3, 1, 1, 2, 3, 2, 12, 1, 4, 7, 1, 1, 1, 1, 2, 2, 6, 1, 3, 2, 1, 5, 2, 2, 6, 2, 13, 1, 1, 1, 2, 6, 2, 5, 2, 1, 3, 1, 3, 1, 1, 2, 1, 20, 2, 7, 1, 2, 2, 3, 2, 1, 16, 58, 3, 1, 2, 2, 6, 1, 2, 1, 2, 1, 9, 2, 3, 1, 4, 1, 13, 2, 1, 1, 4, 2, 1, 3, 6, 2, 2, 1, 1, 1, 1, 23, 1, 6, 3, 6]
leng = 10000
base = 3
rpf = [Dragon(n) for n in range (0,leng)]
rpfBase = [Integer(Mod(rpf[n],base)) for n in range (0,leng)]
rpfNumber = seqToReal(rpfBase,base)
print(rpfNumber)
print(rpfNumber.continued_fraction())

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