115 Algorithmen (Bildungsgesetz) für die Zahlenfolge 0,0,0,1,0,0,1,1,0,1,1,1

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Fortsetzung von https://matheplanet.com/matheplanet/nuke/html/viewtopic.php?topic=250293&start=40
Primitive Algorithmen mit If, oder direkter Binärumwandlung oder ohne Fortsetzung
       
Algor. Beschreibung Link zum Nachrechnen Folge
1 pzktupel: aB[i]=i<6?((i+1)%6==4?1:0):((12-i)%6==4?0:1); Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
11 tactac Haskell: map snd $ tail $ iterate ((`divMod`2).fst) (3784,undefined)
aB[i]=(3784).toString(2).substr(11-i,1); oder b=3784*2;aB[i]=(b>>=1)&1;
Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
15 Scynja: aB[i]=floor((100110111%pow(10,(12-i)))/pow(10,(11-i))) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,0,9,9,9,0,0,0,0,7,7,5,6,5,8,9,7,9,7
48 pzktupel: a=311; Iter: aC[i]=a%2;a=floor(a/2);aB[11-i]=aC[i]; Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1
       
Interpolationen: Polynom, Trigonometrische I.
       
2 https://de.wikipedia.org/wiki/Polynominterpolation
(x-8)*(x-5)*(x-4)*(x-2)*(x-1)*x*(x*(x*(x*(39*x*(2*x-81)+51845)-439475)+1966617)-3772746)/39916800
Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,254,2509,14170,59423,204920,613054,1643798,4037177,9223436,19827678,40461071
3 1/2-cos(PI*x/6)/12-(2+sqrt(3))/12*sin(PI*x/6)-cos(PI*x/3)/12-sin(PI*x/3)/(4*sqrt(3))-cos(PI*x/2)/3-sin(PI*x/2)/3+cos(PI*x*4/6)/4+sin(PI*x*4/6)/(4*sqrt(3))-cos(PI*x*5/6)/12-(2-sqrt(3))/12*sin(PI*x*5/6)-cos(PI*x)/6 Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0
12 sgn(|x*(x*(x*(x*((x-20)*x+145)-470)+664)-380)/60+x|) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
13 sgn(|x*(x*(x*(x*((x-20)*x+145)-470)+664)-260)/60-x|) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
       
Algorithmen mit Modulofunktion (Divisionsrest)
10 viertel: aB[i]=floor((pow(2,floor(i/4)+1)-1)/pow(2,3-(i%4)))%2; Iterationsrechner mit 2 Beispielen 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
22 cramilu: aB[i]=sgn(139230%(i+13)) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0
30 cramilu: aB[i]=1-sgn(((i+1)%4)*((i+1)%7)*((i+1)%10)*((i+1)%11)) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,1
67 bigc(): (13923^11*10)mod(i+13) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,1,1
       
Algorithmen mit https://de.wikipedia.org/wiki/Alias-Effekt
4 aB[i]=floor(sin((i+133)*E*17)*101+101)%2; Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,1,1,1,1,1,0,1,1,0,1,1
61 Table[Mod[Floor[Exp[x]],2],{x,403,444}] wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1
62 Table[Mod[Round[Sqrt[x*E*701]*501+1],2],{x,954,999}] WolframAlpha.com 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,1,1,1,1,1,0,0,1
63 Table[Mod[Round[[x*E]^2*501],2],{x,97,129}] WolframAlpha.com 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,1,1,0,1,0,1
68 Table[Mod[Ceiling[Sin[n/E]*91-Sin[n*Pi]*11]+100,2],{n,179,222}] WolframAlpha.com 0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1
106 Table[Mod[Round[ArcTan[(((50-x)/11) 2)/(1.0000001-((50-x)/11)^2)]*129],2],{x,28,70}]
WolframAlpha.com mit Code
0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0
Algorithmen mit Rekursionen
17 tactac: Fx(x): x<3?0:(x==3?1:max(Fx(x-3),Fx(x-4))) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
16 haegar90: aB=Array(0,0,0,0,0,0,1);i=7; Iter: aB[i]=aB[i-4]+aB[i-3]-aB[i-7];
besser A008679[i]=1+floor((i-3)/3)+floor((3-i)/4);
Iterationsrechner mit Code 0,0,0,0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,2,1,1,2,2,1,2,2,2,2,2,2,3,2,2,3
0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,2,1,1,2,2,1,2,2,2,2,2,2,3,2,2
110 analog zur Primzahlerzeugenden Konstante A249270 kann man auch so eine Konstante für die gesuchte Zahlenfolge kontruieren:
a[0]=34010569 Pi/27899537;Table[a[k]=Floor[a[k-1]]*(FractionalPart[a[k-1]]+1),{k,1,40}];Table[b[k]=Floor[a[k]]-2*k-3,{k,0,39}]

Iterationsrechner mit Code
0,0,0,1,0,0,1,1,0,1,1,1,0,-1,21,58,116,211,326,597,859,1533,2043,2880,3076,3482,5422
111 a[0]=0;co=CoefficientList[Series[1/Cyclotomic[231,x],{x,0,200}],x];Table[a[k]=a[k-1]+co[[k+11]],{k,1,66}] Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,1,1,2,1,1,2,2,1,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
       
       
Algorithmen mit Näherungsfunktion (auch Regression)
14 cramilu: aB[i]=floor(0.6+(c=417690/(i+13))-floor(c));  aC[i]=floor(0.6+(c=417690/(i+13))+floor(c))%2; Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,1,1,0,0,1,0
28 floor(4-pow(x-3,4)/(pow(x-3,4)+1e-3)-2*pow(x-6.5,6)/(pow(x-6.5,6)+2e-2)+atan((x-8.5)*17)/3) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
       
       
Algorithmen mit Pseudozufallsgeneratoren und anderen Iterationen (Fraktale)
23 a=630360016;b=1626622747;c=2147483647; Iter: b=(b*a)%c;aB[i]=b%2; Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,1,1,1,0,1,1,1,1,1,1,1,1
39 Drop[Mod[MandelbrotSetIterationCount[Table[-0.019+0.0000015+I*(y-0.00016),{y,-0.6474,-0.6451,0.0000087}],MaxIterations->1500]+1,2],208]
Mathematica
0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0
46 Lorenz-Attraktor ab Iteration 138
Iterationsrechner mit Code
0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,1,1
49 gonz: aD[0]=6608; Iter: Iter(1,aD[0],0,'false','x=x%2<1?x/2:(x*3+1)/2;','aD[0]=x')%2   0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,1,1,1,1
51 Drop[Mod[JuliaSetIterationCount[0.365-0.37I,Table[x+I*(-0.5),{x,0.19909,0.20619,0.00001}], MaxIterations->5000]+1,2],675]
.
0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0
58 a='218019'; Iter: aB[i]=(Number(a)+1)%2;a='2'+((i+37)*5).toString()+QuerSum(a).toString();   0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,1,0
       
Algorithmen mit Kettenbruch und   (CoefficientList, Series)
31 Table[Abs[SeriesCoefficient[QPochhammer[-x,x^2] EllipticTheta[3,0,-x^4],{x,0,n}]],{n,26,88}]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,2,2,0
35 Drop[CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^10)),{x,0,90}],x],1]   0,0,0,1,0,0,1,1,0,1,1,1,0,2,1,1,1,2,1,2,2,2,1,3,2,2,2,4,2,3,3,4,2,4,4,4,3,5,4,5,4,6,4,6,5,6,5,7,6,7
36 Drop[CoefficientList[Series[Product[1+x^(4i-1),{i,6}]*(1+x^13),{x,0,100}],x],4]   0,0,0,1,0,0,1,1,0,1,1,1,1,0,2,1,1,1,2,2,1,1,3,1,1,2,2,2,1,3,3,2,2,3,2,3,1,3,3,2,2,3,3,2,2,3,3,1,3,2
37 Table[Abs[SeriesCoefficient[Product[(1+x^k) (1-x^(2 k))/(1+x^(4 k)),{k,n}],{x,0,n}]],{n,26,55}]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0
43 ContinuedFraction[(7/9) Pi ArcCos[2632933/3796265]^2,40]-1 www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,7,0,0,3,0,1,4,1,0,0,0,0,6,0
59 ContinuedFraction[784/(81(5+81(Chaitin's Constant)))-11/81,16]-1   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1
60 ContinuedFraction[(3(47(1+sqrt(2))-100))/(11(1+sqrt(2))-1),29]-1   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,2,77,0,2,0,3,3,1
       
Algorithmen mit höheren Funktionen  und Primzahlen
5 aB[i]=1-((Prime(i+990)+1)/2%2);   0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0
8 Table[ Mod[ PartitionsP[n], 2], {n, 26,69,1}]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,1
9 Pari:A309144(n)=ellanalyticrank(ellinit([0,n^2+6*n-3,0,-16*n,0]))[1] https://pari.math.u-bordeaux.fr/gp.html 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,1,2,0,1,0,1,0,1,2,0,1,0,0,0,0
18 Table[Abs[MoebiusMu[n]], {n, 2056, 2088}]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,1,0
19 Table[(LiouvilleLambda[n]+1)/2, {n, 112,139}]   0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,1,0,0,0
20 Table[1 - Mod[Abs[Round[Gamma[Pi/1117-n/200] 121]],2],{n,69,99}]   0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,0,0
32 Table[Mod[Round[AppellF1[Pi/10,Pi/11,Pi/12,13+n,1/(3+n),1/(2+n)]*3^17],2],{n,157,200}]   0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,1,0
34 Table[Mod[Abs[StirlingS2[2*n,n]]+Ceiling[Cos[n*E+1]*191+18],2],{n,951,977}]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,1,0,1,1,0,1,1
38 Table[c=0;Do[If[!PrimeQ[i]&& !PrimeQ[2n-i],c++],{i,1,n,2}];c,{n,2,30}]   0,0,0,1,0,0,1,1,0,1,1,1,1,2,0,2,3,0,2,3,1,2,3,3,2,4,2,3,5
40 Drop[RealDigits[ChampernowneNumber[10],2,115][[1]],87]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,1,1,1,1,1,1,1
44 Drop[Mod[Round[FourierDCT[Table[(1-(x-3)^4/((x-3)^4+1/1000))*3^11,{x,1,177}],3]+800],2],87]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1
45 Table[Sign[Mod[Round[CatalanNumber[n]*E/17],4]],{n,403,444}]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0
47 Drop[Mod[RealDigits[Hypergeometric2F1[1/3, 1/4,3^7/17, 1/7],10,911][[1]],2],887]   0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,1,0,0
52 aB[i]=3070201610190%Prime(i+1);   0,0,0,1,0,0,1,1,0,1,1,1,8,12,32,39,56,33
54 Table[1-Sign[Mod[Abs[BernoulliB[n 2] (n 2+1)!]/2,n^2+2]],{n,576,613}]   0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0,0,1,0
55 Table[Sign[Floor[Mod[Fibonacci[n],n+1]/9]],{n,70,99}]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,1,1
56 Table[1 - Sign[Floor[Mod[CatalanNumber[n],n]/9]],{n,115,144}]   0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,1,0,1,0,0
66 Table[Mod[CarmichaelLambda[n]/2+n+1,2],{n,977,1009}]   0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0
69 Table[Mod[Floor[ArithmeticGeometricMean[1-1/x,1+x]*10³],2],{x,157,200}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,1,1,1
70 Table[Mod[Ceiling[Abs[EllipticNomeQ[n]]*E^(E*7)],2],{n,86,120}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,1,1,1,1,0,1,0,0,1
71 Table[Mod[Round[EulerE[n,n*E]*15/n],2],{n,274,311}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,0,0,0
72 Table[Mod[Round[FresnelC[n/E]*Pi*9133],2],{n,16,49}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1
73 Table[Sign[((GCD[n+13000,33426748355]+1)/2-1)*(PowerMod[2,n,n+1]-1)],{n,598,633}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0
74 Table[Sign[Mod[PartitionsQ[n],3]],{n,805,888,2}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,1
75 Table[Sign[Floor[Mod[LucasL[n],n+72]/13]],{n,67,111}] WolframAlpha 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1
76 Take[SubstitutionSystem[{0->{0,1,0,0},1->{1,1,0,1}},{0},4]//Last,{11,55}] Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0
77 Table[1-Sign[Mod[PrimePi[n 23],3]],{n,16,55}] www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,0,0,0
78 Table[Mod[Floor[3^9/(HypergeometricU[1/3,1/(2*n),1/(3*n)]-11/10)],2],{n,2431,3000,13}] www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,1,0,1,0,0,1,0
79 Table[Mod[Round[(1-(4/9)^(n+1)) Sqrt[3] (7^n/20)],2],{n,185,222}] Koch-Kurven Fläche wolframalpha 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1
80 f[n_]:=FindSequenceFunction[Table[RegionMeasure[SierpinskiCurve[k]],{k,5}],n];Table[Mod[Round[f[n]*39],2],{n,70,99}] Sierpinski curve
Mathematica 11
0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,1,0,1
81 Table[Mod[Round[Abs[ZetaZero[n]]*30],2],{n,57,90}] Riemannsche Vermutung wolframalpha 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0
82 Table[Mod[Round[Abs[AiryBiPrime[n-13/3]]*12],2],{n,44,90}] wolframalpha 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0,1,1,1,0,0,0
83 Flatten[Table[Take[IntegerDigits[x^2+x+17,2],-4],{x,0,11}] ] Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,1,1,0,1,0,1
84 Take[1-Flatten[CellularAutomaton[30,{{1},0},50]],{955,1000}] Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
85 Take[IntegerDigits[BitXor[Floor[Pi*10^99],Floor[E*10^(114)]],2],{147,188}] Pi XOR E -> bin; Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1
86 Take[IntegerDigits[BitOr[Floor[Pi*10^115],Floor[E*10^99]],2],{43,80}] Pi OR E -> bin; Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,0,1,0
87 Take[IntegerDigits[BitAnd[Floor[Pi*10^(122)],Floor[EulerGamma*10^(153)]],2],{303,340}] Pi AND EulerGamma; Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,0
88 Mathematica 12:
Take[Mod[Round[(Flatten[BeveledPolyhedron[Dodecahedron[]][[1]]]+2)*841],2],{164,199}]
Polyhedron-Dodecahedron 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0
89 Mathematica 12:
a=TruncatedPolyhedron[Dodecahedron[]];
Take[Mod[Round[(Flatten[a[[1]]]+2)*294],2],{3,40}]
TruncatedPolyhedron-Dodecahedron 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,1,1,1,1,1,1,0
90 Mathematica 12:
a=AugmentedPolyhedron[Dodecahedron[]];
Take[Mod[Floor[(Flatten[a[[1]]]+2)*1238],2] ,{20,50}]
AugmentedPolyhedron-Dodecahedron 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,1,0
91 Take[IntegerDigits[Hash[ByteArray[Table[n*14,{n,10}]],"SHA256"],2],{146,180}] Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1
92 Take[IntegerDigits[Hash[ByteArray[Table[n+64,{n,10}]],"SHA256SHA256"],2],{63,100}] Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0
93 Take[IntegerDigits[Hash[ByteArray[Table[n+118,{n,10}]],"SHA384"],2],{42,80}] Mathematica 12 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1
94 Take[IntegerDigits[Hash[ByteArray[Table[n+32,{n,10}]],"SHA512"],2],{66,99}] Mathematica 12 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,1,1,1,0,1
95 Take[IntegerDigits[Hash[ByteArray[Table[n+40,{n,10}]],"SHA3-256"],2],{197,233}] Mathematica 12 0,0,0,1,0,0,1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,0,1,1,1,1,0,1,1,0,1
96 Take[IntegerDigits[Hash[ByteArray[Table[n+13,{n,10}]],"Keccak256"],2],{53,90}] Mathematica 12 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1
97 Take[RealDigits[GoldenRatio*395,3,777][[1]],{527,569}] Goldener Schnitt Basis 3; Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,2,0,1,1,1,2,2,2,2,0,1,1,1,2,1,0,0,2,2,0,2,1,0,0,1,0,1,1,2,0,0
98 Take[RealDigits[Zeta[5]*4142,4,444][[1]],{308,350}] Zeta(5) Basis 4; Mathematica 11 0,0,0,1,0,0,1,1,0,1,1,1,3,1,2,2,3,3,3,0,3,1,1,0,3,2,3,0,2,2,1,0,0,3,0,3,3,0,0,2,2,2,2
99 Take[RealDigits[(8*Pi-18*ArcCos[1/3])*39369,5,900][[1]],{842,880}] Reuleaux Tetrahedron Fläche Basis 5 0,0,0,1,0,0,1,1,0,1,1,1,4,1,0,4,0,4,4,1,3,3,3,1,1,4,2,3,4,4,1,2,1,3,3,1,2,4,1
100 Take[RealDigits[Gamma[1/3]*Gamma[5/6]/Gamma[1/6]*444561,6,1070][[1]],{1005,1046}] A081760=Landau's const. Basis 6 0,0,0,1,0,0,1,1,0,1,1,1,2,4,5,5,5,3,3,3,3,4,0,0,0,4,0,0,5,2,5,1,3,3,2,0,4,4,5,5,0,4
101 Table[Mod[Floor[CDF[HypergeometricDistribution[10,50,100],x]*(E+1789)],2],{x,33}] kum. hypergeometrische Verteilungsfunkt. 0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
102 Table[Mod[Floor[CDF[BinomialDistribution[40,27/100],x]*(E+1798)],2],{x,4,33}] kumulierte Binomialverteilungsfunktion 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
103 haribo's Idee:
Alph01=morseAlphabet={"._","_...",...;StringReplace[morseAlphabet,{"."->"0","_"->"1"}];
ToCharacterCode[StringJoin[Characters["IRWAM"]/.Thread[Table
[FromCharacterCode[k+64],{k,26}]->Alph01]]]-48
Mathematica morse-code
0,0,0,1,0,0,1,1,0,1,1,1
104 Table[Mod[Round[Abs[MeijerG[{{},{(3+x)/2,(4+x)/2}},{{1,1,3/2},{1/2}},x^2/16]]*1000119],2],{x,8/10,6,1/10}] MeijerG Funktion 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0,0,0,1,1,1,0
105 Take[Flatten[Table[Boole[!CoprimeQ[i,j,77]],{i,99},{j,99}]],{488,533}] Teilerfremdheit als 3D-Würfel Teilerfremd-Würfel
0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,1,1,0,1
107 Take[ShiftRegisterSequence[{12,{2,1}}],{1496,1540}] Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,1,1,1
108 Take[DeBruijnSequence[{0,1},12],{1662,1711}] Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,1,0,1,0,0
109 Take[Flatten[Tuples[{0,1},11]],{3421,3466}] Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0
112 atomicRadiusData=DeleteMissing[EntityValue[Take[EntityList["Element"],{1,54}],{EntityProperty["Element","AtomicNumber"],EntityProperty["Element", "AtomicRadius"]},"EntityAssociation"]];
Table[Mod[Round[atomicRadiusData[[k]][[2]][[1]]*E*227],2],{k,8,54}]
Mathematica: Atomradien Atom Radien
0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,1,0,0,0,1,1,1
113 Table[Mod[Floor[CDF[GompertzMakehamDistribution[0.3,1],x]*1107],2],{x,6/10,5,1/10}] GompertzMakehamDistribution 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0
114 Table[Mod[Floor[Erf[(x-1)/78]*15018],2],{x,41,53,1/4}] wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0,1,1,0,1,1,1,1,1,1,1,0,1,1,0,1
115 Table[Mod[Floor[CDF[ErlangDistribution[5,0.3],x]*2750],2],{x,5/2,14,1/4}] Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0,1,1,1,1
       
Algorithmen mit Nachkommastellen
6 ((43*PI)/1349399).toString().substr(i+2,1) Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,3,1,9,4,5,4,8,9,0,1,0,5,8,1,2,7,8,4,4,1,8
7 Number(GetPiDezi(i+1442,1))%2; //Pi Nachkommastellen Mod 2 Iterationsrechner mit Code 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0
21 Drop[RealDigits[Pi, 2, 375][[1]],306] (*binäre Pi Nachkommastellen*)   0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1
24 Drop[IntegerDigits[(2^281*43 + 1)/32615343, 2],78] (*ganze Zahl*)   0,0,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0,1,0,0,1,0,0,0,1,0,0,1
25 Drop[RealDigits[Pi*6663710/19456209,2,75][[1]],1]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
26 Pi-Pos=28224389850560;aB[i]=Number(('541863910859752494241555455445444').substr(32-i,1))-4; Iterationsrechner & pi-suche 0,0,0,1,0,0,1,1,0,1,1,1,-3,0,-2,0,5,0,-2,1,3,5,1,4,-4,-3,5,-1,2,4,-3,0,1
27 Pi-Pos=128917826590;aB[i]=Number(('60079425684445445545550557269761542825').substr(10+i,1))-4; lamprechts.de../pi-Nachkommastellen-suche 0,0,0,1,0,0,1,1,0,1,1,1,-4,1,1,3,-2,2,5,3,2,-3,1,0,-2,4,-2,1,-4,-4,-4,-4
29 Pos=11011785426942; GetPiDezi(11011785426942,..) lamprechts.de../pi-Nachkommastellen-suche 0,0,0,1,0,0,1,1,0,1,1,1,9,5,9,8,8,4,6,7,8,3,6,0,3,1,6,1,4,8,9,2,0,0,8,1,2,4
33 Pos=11284760662796; GetPiDezi(11284760662796,..) lamprechts.de../pi-Nachkommastellen-suche 0,0,0,1,0,0,1,1,0,1,1,1,6,6,8,5,2,1,0,8,2,9,4,0,8,3,6,4,9,1,7,4,6,9,2,8,8
41 Drop[RealDigits[EulerGamma,2,2500][[1]],2467] https://www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0
42 Drop[RealDigits[Sqrt[2],2,915][[1]],886] https://www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0
57 Pos=12585415521704; GetPiDezi(12585415521704,..) lamprechts.de../pi-Nachkommastellen-suche 0,0,0,1,0,0,1,1,0,1,1,1,7,2,0,8,6,3,0,4,3,6,8,5,2,8,5,4,7,8,1,0,7,0,2,6,0,7
       
Algorithmen mit Differenzialgleichungen oder numerischer Integration
50 s=DSolve[{y'[x]+y[x]==111*Sin[x],y[0]==1/E},y[x],x];Table[Mod[Ceiling[(N[y[x]/.s[[1]],22])+E^Pi*4],2],{x,114,129,1/2}]   0,0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,1,0,1,0,1,0,1,1,1,1,0,1,0,1,1
53 m1=13.0000001;m2=13.0000002;m3=13.0000003;nds=NDSolve[{x1'[t]==vx1[t],y1'[t]==vy1[t],x2'[t]==vx2[t],
y2'[t]==vy2[t],x3'[t]==vx3[t],y3'[t]==vy3[t],m1 vx1'[t]==-((m1 m2(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(m1 m3(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),m1 vy1'[t]==-((m1 m2(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(m1 m3(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),m2 vx2'[t]==(m1 m2(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(m2 m3(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),m2 vy2'[t]==(m1 m2(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(m2 m3(y2[t]-y3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),m3 vx3'[t]==(m1 m3(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(m2 m3(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),m3 vy3'[t]==(m1 m3(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(m2 m3(y2[t]-y3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),x1[0]==0.7,y1[0]==-0.5,x2[0]==-0.7,y2[0]==2,x3[0]==0,y3[0]==0,vx1[0]==0.93240737/2,vy1[0]==
0.86473146/2,vx2[0]==0.93240737/2,vy2[0]==0.86473146/2,vx3[0]==-0.93240737,vy3[0]==-0.86473146},{x1,x2,x3,y1,y2,y3,vx1,vx2,vx3,vy1,vy2,vy3},{t,0,16}];
wikipedia.../Dreikörperproblem
Mathematica:
Drop[Table[Mod
[Round[(N[x3[t]/.nds[[1]],14]+
4)*77],2],{t,0,5,0.07}],40]

0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,1,1,0,1,0
64 1-Drop[RealDigits[NIntegrate[x^x, {x,4,5}, WorkingPrecision -> 200],2][[1]],554] https://www.wolframalpha.com/input/? 0,0,0,1,0,0,1,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1
65 Drop[Table[Mod[Round[N[ArcLength[{Cos[t (3+Pi/1000)],Sin[3 t]},{t,0,n}],33]*101]+1,2],{n,103.214,131,1.001}],2] Lissajous Bogenlänge Mathematica 0,0,0,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0,0
Weitere Zahlenfolgen

Stand: 28.11.2020
Algorithmen: 115 Stück
Gerd Lamprecht