MP: Zahlenfolge 0,0,0,1,0,0,1,1,0,1,1,1 (Forum Matroids Matheplanet)

In[49]:= Table[Abs[SeriesCoefficient[QPochhammer[-x,x^2] EllipticTheta[3,0,-x^4],{x,0,n}]],{n,26,88}] Out[49]= {0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,2,2,0,1,1,1,0,1,1,1,0,0,1,1,0,0,2,1,1,1,2,1,0,1,1} In[43]:= Table[Mod[Round[AppellF1[Pi/10,Pi/11,Pi/12,13+n,1/(3+n),1/(2+n)]*3^17],2],{n,157,200}] Out[43]= {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}

In[118]:= Table[Mod[Abs[StirlingS2[2*n,n]]+Ceiling[Cos[n*E+1]*191+18],2],{n,951,977}] Out[118]= {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} In[135]:= Drop[CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^10)),{x,0,90}],x],1] Out[135]= {0,0,0,1,0,0,1,1,0,1,1,1,0,2,1,1,1,2,1,2,2,2,1,3,2,2,2,4,2,3,3,4,2,4,4,4,3,5,4,5,4,6,4,6,5,6,5,7,6,7,6,8,6,8,7,9,7,9,8,10,8,10,9,11,9,11,10,12,10,13,11,13,11,14,12,14,13,15,13,16,14,16,14,18,15,17,16,19,16,19} In[133]:= Drop[CoefficientList[Series[Product[1+x^(4i-1),{i,6}]*(1+x^13),{x,0,100}],x],4] Out[133]= {0,0,0,1,0,0,1,1,0,1,1,1,1,0,2,1,1,1,2,2,1,1,3,1,1,2,2,2,1,3,3,2,2,3,2,3,1,3,3,2,2,3,3,2,2,3,3,1,3,2,3,2,2,3,3,1,2,2,2,1,1,3,1,1,2,2,1,1,1,2,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1} In[124]:= Table[Abs[SeriesCoefficient[Product[(1+x^k) (1-x^(2 k))/(1+x^(4 k)),{k,n}],{x,0,n}]],{n,26,55}] Out[124]= {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}

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} Drop[Mod[MandelbrotSetIterationCount[Table[-0.019+0.0000015+I*(y-0.00016),{y,-0.6474000000000,-0.6451000000000,0.0000087}],MaxIterations->1500]+1,2],208] ={0,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,1,1,1,0,1}

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} Drop[RealDigits[EulerGamma,2,2500][[1]],2467] = {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} Drop[RealDigits[Sqrt[2],2,915][[1]],886] = {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}

ContinuedFraction[(7/9) Pi ArcCos[2632933/3796265]^2,40]-1 Out[66]= {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} Drop[Mod[Round[FourierDCT[Table[(1-(x-3)^4/((x-3)^4+1/1000))*3^11,{x,1,177}],3]+800],2],87] Out[67]= {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,..

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],13.0000001 vx1'[t]==-((13.0000001 13.0000002(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(13.0000001 13.0000003(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),13.0000001 vy1'[t]==-((13.0000001 13.0000002(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(13.0000001 13.0000003(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),13.0000002 vx2'[t]==(13.0000001 13.0000002(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(13.0000002 13.0000003(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000002 vy2'[t]==(13.0000001 13.0000002(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(13.0000002 13.0000003(y2[t]-y3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000003 vx3'[t]==(13.0000001 13.0000003(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(13.0000002 13.0000003(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000003 vy3'[t]==(13.0000001 13.0000003(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(13.0000002 13.0000003(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}];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],13.0000001 vx1'[t]==-((13.0000001 13.0000002(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(13.0000001 13.0000003(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),13.0000001 vy1'[t]==-((13.0000001 13.0000002(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2))-(13.0000001 13.0000003(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2),13.0000002 vx2'[t]==(13.0000001 13.0000002(x1[t]-x2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(13.0000002 13.0000003(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000002 vy2'[t]==(13.0000001 13.0000002(y1[t]-y2[t]))/((x1[t]-x2[t])^2+(y1[t]-y2[t])^2)^(3/2)-(13.0000002 13.0000003(y2[t]-y3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000003 vx3'[t]==(13.0000001 13.0000003(x1[t]-x3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(13.0000002 13.0000003(x2[t]-x3[t]))/((x2[t]-x3[t])^2+(y2[t]-y3[t])^2)^(3/2),13.0000003 vy3'[t]==(13.0000001 13.0000003(y1[t]-y3[t]))/((x1[t]-x3[t])^2+(y1[t]-y3[t])^2)^(3/2)+(13.0000002 13.0000003(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}];

CDF[HypergeometricDistribution[n,50,100],x] Out: 1-(925017065282507919013470723235883682349486807421901987706139271018810570717360434442383213140448215302144000000000000000000000000 HypergeometricPFQRegularized[{1,1-n+Floor[x],-49+Floor[x]},{2+Floor[x],52-n+Floor[x]},1])/(Binomial[100,n] (49-Floor[x])! (-1+n-Floor[x])!)

morseAlphabet={"._","_...","_._.","_..",".",... Alph01=StringReplace[morseAlphabet,{"."->"0","_"->"1"}] ToCharacterCode[StringJoin[Characters["IRWAM"]/.Thread[Table[FromCharacterCode[k+64],{k,26}]->Alph01]]]-48 Out[31]= {0,0,0,1,0,0,1,1,0,1,1,1}