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

1,136

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(2^n) = 1.

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A070165, A187203.

Sequence in context: A189289 A270885 A353682 * A127972 A103451 A103452

Adjacent sequences: A359244 A359245 A359246 * A359248 A359249 A359250

Keyword

nonn

Author

Michel Lagneau, Dec 22 2022

Status

approved