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.
%I A359247 #32 Jan 09 2023 02:25:18 %S A359247 1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,1,1,1,1,0,0,0,1,1,1,1,0, %T A359247 1,1,0,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,0,1,0, %U A359247 0,1,0,0,0,0,1,1,1,1,1,1,0,1,0,1,0,1,1,1,0,0 %N A359247 The bottom entry in the absolute difference triangle of the elements in the Collatz trajectory of n. %H A359247 Michel Lagneau, <a href="/A359247/b359247.txt">Table of n, a(n) for n = 1..10000</a> %H A359247 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %F A359247 a(2^n) = 1. %e A359247 a(3) = 1 because the Collatz trajectory of 3 is T = [3, 10, 5, 16, 8, 4, 2, 1], and the absolute difference triangle of the elements of T is: %e A359247 3 . 10 . 5 . 16 . 8 . 4 . 2 . 1 %e A359247 7 . 5 . 11 . 8 . 4 . 2 . 1 %e A359247 2 . 6 . 3 . 4 . 2 . 1 %e A359247 4 . 3 . 1 . 2 . 1 %e A359247 1 . 2 . 1 . 1 %e A359247 1 . 1 . 0 %e A359247 0 . 1 %e A359247 1 %e A359247 with bottom entry a(3) = 1. %t A359247 Collatz[n_]:=NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&];Flatten[Table[Collatz[n],{n,10}]];Table[d=Collatz[m];While[Length[d]>1,d=Abs[Differences[d]]];d[[1]],{m,100}] %o A359247 (PARI) a(n) = my(list=List([n])); while (n!=1, if(n%2, n=3*n+1, n=n/2); listput(list, n)); my(v = Vec(list)); while (#v != 1, v = vector(#v-1, k, abs(v[k+1]-v[k]))); v[1]; \\ _Michel Marcus_, Dec 23 2022 %Y A359247 Cf. A070165, A187203. %K A359247 nonn %O A359247 1,136 %A A359247 _Michel Lagneau_, Dec 22 2022