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

Author

Rémy Sigrist, Dec 22 2022

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A358668, A359194, A359226.

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

Programs

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 *)

PARI

See Links section.

Formula

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

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