Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Combinatorics
XXXX.
In[1]:=
XXXX
Out[1]=
XXXX
Inverse Fibonacci of 4 million.
In[3]:=
 | InverseFibonacci |
Out[3]=
33.3
…
In[4]:=
N
[4000000],40
 | InverseFibonacci |
Out[4]=
33.26294791969964592662685263812261664648
In[5]:=
Select[EvenQ]FibonacciRangeFloor
[4000000]
 | InverseFibonacci |
Out[5]=
{2,8,34,144,610,2584,10946,46368,196418,832040,3524578}
In[6]:=
AccumulateSelect[EvenQ]FibonacciRangeFloor
[4000000]
 | InverseFibonacci |
Out[6]=
{2,10,44,188,798,3382,14328,60696,257114,1089154,4613732}
In[7]:=
StringRiffleAccumulateSelect[EvenQ]FibonacciRangeFloor
[4000000]," "
| InverseFibonacci |
Out[7]=
2 10 44 188 798 3382 14328 60696 257114 1089154 4613732
In[8]:=
CopyToClipboardStringRiffleAccumulateSelect[EvenQ]FibonacciRangeFloor
[4000000]," "
| InverseFibonacci |
In[10]:=
CoefficientListSeries,{x,0,40},x
2x
(1-x)(--4x+1)
2
x
Out[10]=
{0,2,10,44,188,798,3382,14328,60696,257114,1089154,4613732,19544084,82790070,350704366,1485607536,6293134512,26658145586,112925716858,478361013020,2026369768940,8583840088782,36361730124070,154030760585064,652484772464328,2763969850442378,11708364174233842,49597426547377748,210098070363744836,889989708002357094,3770056902373173214,15970217317495049952,67650926172353373024,286573922006908542050,1213946614199987541226,5142360378806858706956,21783388129427422369052,92275912896516548183166,390887039715493615101718,1655824071758491008590040,7014183326749457649461880}
In[11]:=
LinearRecurrence[{5,-3,-1},{0,2,10},30]
Out[11]=
{0,2,10,44,188,798,3382,14328,60696,257114,1089154,4613732,19544084,82790070,350704366,1485607536,6293134512,26658145586,112925716858,478361013020,2026369768940,8583840088782,36361730124070,154030760585064,652484772464328,2763969850442378,11708364174233842,49597426547377748,210098070363744836,889989708002357094}
Install the Paclet
In[32]:=
PacletSiteUpdate[PacletSites[]]
Out[32]=
{PacletSiteObject[URLhttps://pacletserver.wolfram.com,NameWolfram Research Paclet Server,LocalFalse,TypeServer],PacletSiteObject[URLhttps://resources.wolframcloud.com/PacletRepository/pacletsite,NameWolfram Paclet Repository,LocalFalse,TypeServer]}
In[33]:=
PacletInstall["PeterBurbery/Combinatorics"]
Out[33]=
PacletObject
 |  |
|
In[19]:=
SystemOpen["C:\\Users\\Peter\\AppData\\Roaming\\Mathematica\\Paclets\\Repository\\PeterBurbery__Combinatorics-2.0.3"]
In[2]:=
| PermutationFromIndex |
Out[2]=
PeterBurbery`Combinatorics`PermutationFromIndex[1000000,10]
In[1]:=
Needs["PeterBurbery`Combinatorics`"]
In[35]:=
Quit[]
In[3]:=
Accumulate[Prime[Range[10]]]
Out[3]=
{2,5,10,17,28,41,58,77,100,129}
In[4]:=
InverseFunction[PrimePi][2000000]
Out[4]=
32452843
In[6]:=
Prime[InverseFunction[PrimePi][2000000]]
Out[6]=
622826473
In[5]:=
Total@Range[InverseFunction[PrimePi][2000000]]
Out[5]=
526593525617746
In[7]:=
PrimePi[2000000]
Out[7]=
148933
In[8]:=
Sum[Prime[n],{n,PrimePi[2000000]}]
Out[8]=
142913828922
In[9]:=
PolygonalNumber[Range[10]]
Out[9]=
{1,3,6,10,15,21,28,36,45,55}
In[11]:=
DivisorSigma[0,PolygonalNumber[Range[20]]]
Out[11]=
{1,2,4,4,4,4,6,9,6,4,8,8,4,8,16,8,6,6,8,16}
In[12]:=
CopyToClipboard[StringRiffle[DivisorSigma[0,PolygonalNumber[Range[20]]]," "]]
In[13]:=
Binomial[20+20,20]
Out[13]=
137846528820
In[14]:=
Total[IntegerDigits[]]
1000
2
Out[14]=
1366
In[15]:=
s[n_]:=DivisorSigma[1,n]-n;AmicableNumberQ[n_]:=If[Nest[s,n,2]n&&!s[n]n,True,False];Select[Range[10^6],AmicableNumberQ[#]&](*AntKing,Jan022007*)
Out[15]=
{220,284,1184,1210,2620,2924,5020,5564,6232,6368,10744,10856,12285,14595,17296,18416,63020,66928,66992,67095,69615,71145,76084,79750,87633,88730,100485,122265,122368,123152,124155,139815,141664,142310,153176,168730,171856,176272,176336,180848,185368,196724,202444,203432,280540,308620,319550,356408,365084,389924,399592,430402,437456,455344,469028,486178,503056,514736,522405,525915,600392,609928,624184,635624,643336,652664,667964,669688,686072,691256,712216,726104,783556,796696,802725,863835,879712,898216,901424,947835,980984,998104}
In[16]:=
s[n_]:=DivisorSigma[1,n]-n;AmicableNumberQ[n_]:=If[Nest[s,n,2]n&&!s[n]n,True,False];Select[Range[10^4],AmicableNumberQ[#]&](*AntKing,Jan022007*)
Out[16]=
{220,284,1184,1210,2620,2924,5020,5564,6232,6368}
In[17]:=
s[n_]:=DivisorSigma[1,n]-n;AmicableNumberQ[n_]:=If[Nest[s,n,2]n&&!s[n]n,True,False];Total@Select[Range[10^4],AmicableNumberQ[#]&](*AntKing,Jan022007*)
Out[17]=
31626
In[18]:=
Total[Join[Reap[For[n=1,n≤10^4,n++,If[(s=DivisorSigma[1,n])>2n&&DivisorSigma[1,s-n]s,Sow[n]]]]〚2,1〛(*A002025Smallerofanamicablepair:(a,b)suchthatsigma(a)=sigma(b)=a+b,a<b.*),Reap[For[n=1,n≤10^4,n++,If[(s=DivisorSigma[1,n])<2n&&DivisorSigma[1,s-n]s,Sow[n]]]]〚2,1〛(*A002046Largerofamicablepair.*)]]
Out[18]=
31626
In[30]:=
Prime[10001]
Out[30]=
104743
In[115]:=
FromDigits
[,10]-1
| PermutationFromIndex |
6
10
Out[115]=
2783915460
""