A359657 Least k such that A359247(k) = n, or 0 if no such k exists.

5, 1, 136, 168, 141, 424, 1867, 680, 3981, 5800, 2216, 13648, 5763, 2728, 8872, 11944, 15752, 6824, 15219, 8352, 17064, 10920, 10400, 38407, 25105, 27304, 36879, 40501, 37077, 20323, 25635, 29073, 57611, 45795, 90197, 61741, 68735, 55319, 46645, 42549, 95412

Offset

0,1

Comments

Or least k such that the bottom entry in the absolute difference triangle of the elements in the Collatz trajectory of k is equal to n, or 0 if no such k exists.

Links

Table of n, a(n) for n=0..40.

Example

a(3) = 168 because the Collatz trajectory of 168 is T = 168 -> 84 -> 42 -> 21 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1  and the absolute difference triangle of the elements of T is:
   168  84  42  21  64  32  16  8  4  2  1
    84, 42, 21, 43, 32, 16,  8, 4, 2, 1
    42, 21, 22, 11, 16,  8,  4, 2, 1
    21,  1, 11,  5,  8,  4,  2, 1
    20, 10,  6,  3,  4,  2,  1
    10,  4,  3,  1,  2,  1
     6,  1,  2,  1,  1
     5,  1,  1,  0
     4,  0,  1
     4,  1
     3
with bottom entry = A359247(168) = 3.

Mathematica

nn=20000; Collatz[n_]:=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; Flatten[Table[Collatz[n], {n, nn}]]; Do[k=1; Table[d=Collatz[m]; While[Length[d]>1, d=Abs[Differences[d]]]; If[d[[1]]==u&&k==1, Print[u, " ", m]; k=0], {m, nn}], {u, 0, 22}]

Crossrefs

Cf. A070165, A187203, A359247.

Sequence in context: A356051 A099740 A362161 * A133002 A272755 A293572

Adjacent sequences: A359654 A359655 A359656 * A359658 A359659 A359660

Keyword

nonn

Author

Michel Lagneau, Jan 10 2023

Status

approved