In[]:=
PrintTemporary[Style["Define the following.","Title"],3];PrintTemporary[WolframAlpha["MRB constant definition",{{"DefinitionPod:MathWorldData",1},"ComputableData"}]];CloudGet["https://www.wolframcloud.com/obj/ed331fd0-6500-46bf-bb3b-c32faadec459"];Pause[8];​​x=Input["Counting the 0 in 0., wHich digitof the MRB constant do youy want?"];T0=SessionTime[];Print["Digit ",x," is ",t=ResourceFunction["NthDigit"][Rationalize[m,0],x]];mt=Rationalize[m,10^-(x+20)];mm=N[mt,x-1];Print["See it in full context by entering mm."];Print["Spigot took ",SessionTime[]-T0," seconds"]
Digit 777 is 7
See it in full context by entering mm.
Spigot took 0.9875444 seconds
Check by manual computation of all previous digits.
In[]:=
NSum[
n
(-1)
(
1/n
n
-1),{n,1,Infinity},Method"AlternatingSigns",WorkingPrecision->x+10]
Out[]=
0.18785964246206712024851793405427323005590309490013878617200468408947723156466021370329665443310749690384234585625801906123137009475922663043892934889618412083733662608161360273812637937343528321255276396217148932170207628206217151671540841268044836354167199851976802527598938993914457983505561350964852107120784442309586812949768852694956420425558648367044104252795247106066609263397483410311578167864166891546003422225883800254553968929471142122189105098328712277308020036445215390536395055332203470627551159812828039510219264914673176293516190659816018664245824950697203381992958420935515162514399357600764593291281451709082424915883204169066409334435914806705564692806787007028115009380606938139385953360657987405562062348704329360737819564603104763950664893061360645528067515193490
In[]:=
MRB1=NSum[
n
(-1)
(
1/n
n
-1),{n,1,Infinity},Method"AlternatingSigns",WorkingPrecision->x+10];​​Print["The first ",x,Style["+up to 10(that may be subject to rounding error)",Large]," digits are ",N[MRB1,x+10]];Print[" and you extracted ",Style[t,Red]]
The first 777+up to 10(that may be subject to rounding error) digits are 0.18785964246206712024851793405427323005590309490013878617200468408947723156466021370329665443310749690384234585625801906123137009475922663043892934889618412083733662608161360273812637937343528321255276396217148932170207628206217151671540841268044836354167199851976802527598938993914457983505561350964852107120784442309586812949768852694956420425558648367044104252795247106066609263397483410311578167864166891546003422225883800254553968929471142122189105098328712277308020036445215390536395055332203470627551159812828039510219264914673176293516190659816018664245824950697203381992958420935515162514399357600764593291281451709082424915883204169066409334435914806705564692806787007028115009380606938139385953360657987405562062348704329360737819564603104763950664893061360645528067515193490
and you extracted 7