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
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
Programs
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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 *)
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PARI
See Links section.
Formula
a(n) = 0 iff A358668(n) = n.
a(3*n+2) = 0. - Thomas Scheuerle, Dec 22 2022