A359247 The bottom entry in the absolute difference triangle of the elements in the Collatz trajectory of n.

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, 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, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0

Offset: 1

Author

Michel Lagneau, Dec 22 2022

Keywords

• nonn

Examples

			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:
  3  . 10  .  5  . 16  .  8  .  4  .  2  .  1
     7  .  5  . 11  .  8  .  4  .  2  .  1
        2  .  6  .  3  .  4  .  2  .  1
           4  .  3  .  1  .  2  .  1
              1  .  2  .  1  .  1
                 1  .  1  .  0
                    0  .  1
                       1
with bottom entry a(3) = 1.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A070165, A187203.

Programs

Mathematica

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}]

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

Formula

a(2^n) = 1.