This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a355240(upto) = {my(D=List()); for (start=5, upto, my(old=start,new=0,L=0);while (abs(new-start)>1 && new!=1, L++; if(old%2==0,new=old/2,new=3*old+1);old=new); if(new>1, listput(~D,L))); Set(D)};
a355240(10000)
8 is a term because the orbit started at 8 - 1 = 7 reaches 8: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8; 10 is a term because it is in the orbit starting at 10 - 1 = 9: 9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10.
collatz(start,target) = {my(old=start,new=0); while (new!=target && new!=1, if(old%2==0, new=old/2, new=3*old+1); old=new); new>1};
for (k=5, 10000, if(collatz(k-1,k), print1(k,", ")))
a(1) = 5 because the orbit started at 6 = a(1) + 1 reaches 5: 6 -> 3 -> 10 -> 5; a(2) = 8 because the orbit started at 9 = a(2) + 1 reaches 8: 9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8; a(3) = 10 because the orbit started at 11 = a(3) + 1 reaches 10: 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10.
collatz(start, target) = {my(old=start, new=0); while (new!=target && new!=1, if(old%2==0, new=old/2, new=3*old+1); old=new); new>1};
for (k=5, 10000, if(collatz(k+1, k), print1(k, ", ")))
a(4)=2 because the number closest to 4 in Collatz trajectory of 4 is 2.
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Join[{0}, Table[Min[Rest[Abs[Collatz[n] - n]]], {n, 2, 100}]]
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