A359214 a(n) is the least k >= 0 such that A359194^k(A358668(n)) = n (where A359194^k denotes the k-th iterate of A359194).

0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 4, 3, 0, 5, 0, 0, 1, 74, 0, 3, 7, 0, 1, 0, 0, 1, 5, 0, 0, 6, 0, 0, 2, 0, 77, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 8, 0, 0, 4, 0, 9, 1, 0, 0, 75, 0, 7, 6, 0, 8, 0, 0, 1, 0, 0, 76, 0, 0, 1, 5418, 0, 1, 0, 0, 2, 0, 0

Offset

0,14

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Formula

a(n) = 0 iff A358668(n) = n.

a(3*n+2) = 0. - Thomas Scheuerle, Dec 22 2022

Example

The orbit of 0 under repeated application of A359194 is:
    0, 1, 0, ...
So a(0) = 0, a(1) = 1.
The orbit of 2 under repeated application of A359194 is:
    2, 1, 0, 1, 0, ...
So a(2) = 0.
The orbit of 3 under repeated application of A359194 is:
    3, 6, 13, 24, 55, 90, 241, 300, 123, 142, 85, 0, 1, 0, ...
So a(3) = 0, a(6) = 1, a(13) = 2, a(24) = 3, a(55) = 4, etc.

Mathematica

nn = 83; c[_] = -1; c[0] = 0; f[n_] := FromDigits[BitXor[1, IntegerDigits[3*n, 2]], 2]; Do[(MapIndexed[If[c[#1] == -1, Set[c[#1], First[#2] - 1]] &, #]; -1 + Length[#]) &@ NestWhileList[f, n, c[#] == -1 && # > 1 &], {n, 0, nn}]; Array[c, nn] (* Michael De Vlieger, Dec 23 2022 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A358668, A359194, A359226.

Cf. A343858 (smallest numbers inside cyclic trajectories of the generalized Collatz function bx+c).

Sequence in context: A145382 A192423 A368667 * A265584 A360205 A078909

Adjacent sequences: A359211 A359212 A359213 * A359215 A359216 A359217

Keyword

nonn,base

Author

Rémy Sigrist, Dec 22 2022

Status

approved