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(*MikkHeidema'sRecamanSeqfromOEISA005132*)RecamanSeq[i_Integer]:=Fold[With[{lst=Last@#,len=Length@#},Append[#,If[lst>len&&!MemberQ[#,lst-len],lst-len,lst+len]]]&,{0},Range@i];
Define a function that links adjacent items with a semi-circle based on their lexicographic order:
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semiCircularPath[{u_Integer,v_Integer}]:=Withmid=Midpoint[{{u,u},{v,v}}],r=
2
Abs[u-v]2,If[u>v,Circle[mid,r,{-3π/4,π/4}],Circle[mid,r,{π/4,5*π/4}]]Link all adjacent pairs with the corresponding semi-circles:
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paths=semiCircularPath/@Partition[RecamanSeq[800],2,1];
Use AxisObject to add an axis along the diagonal line in the graphics. Wrap everything in the Manipulate function:
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Manipulate[Graphics[{AxisObject[Line[{{0,0},2*{n,n}}],{0,2*n}],StandardOrange,paths[[1;;n]]},PlotRange->{{-.15n,2n},{-.15n,2*n}},ImagePadding->8,ImageSize->600,Background->Black],{{n,277},1,500,1},SaveDefinitions->True]
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Create animation and save to a local “.mov” file:
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LaunchKernels[];
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frames=ParallelTable[Image@Graphics[{AxisObject[Line[{{0,0},2*{n,n}}],{0,2*n}],StandardOrange,paths[[1;;n]]},PlotRange->{{-.15n,2n},{-.15n,2*n}},ImagePadding->8,ImageSize->400],{n,1,400}];
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Export["rq.mov",frames]
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rq.mov
Click to play the spooky audio from the numbers:
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keys=Mod[RecamanSeq[1000],48];
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SeedRandom["Recaman"];
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so=Sound[{SoundNote[#,RandomChoice[{0.1,0.2,0.05,0.06,0.07}],SoundVolume->RandomReal[{.5,1}]]&/@keys}]
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Sound note overlap allowed:
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SeedRandom["Recaman"];duration=RandomChoice[{0.1,0.2,0.05,0.06,0.07},1001];tInit=Accumulate[duration];Sound[MapThread[SoundNote[#,{#2,#2+#3}+RandomReal[{-0.1,0.05}],SoundVolume->RandomReal[{.3,1}]]&,{keys,tInit,duration}]]
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CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Recamán's sequence, semi circles and spooky sound
by Shenghui Yang
Wolfram Community, STAFF PICKS, October 26, 2025
https://community.wolfram.com/groups/-/m/t/3565570
by Shenghui Yang
Wolfram Community, STAFF PICKS, October 26, 2025
https://community.wolfram.com/groups/-/m/t/3565570