A349250 Size of the orbit of n under iterations of the digit-census function A348783.
8, 7, 5, 10, 12, 14, 16, 18, 20, 22, 6, 5, 3, 8, 10, 12, 14, 16, 18, 20, 4, 2, 6, 8, 10, 12, 14, 16, 18, 20, 6, 8, 8, 12, 10, 12, 14, 16, 18, 20, 10, 10, 10, 10, 12, 12, 14, 16, 18, 20, 12, 12, 12, 12, 12, 16, 14, 16, 18, 20, 14, 14, 14, 14, 14, 14, 14, 16, 18, 20
Offset: 0
Examples
Under iterations of A348783, 0 -> 1 -> 10 -> 11 -> 20 -> 101 -> 21 -> 110 -> 21 -> ...: here, the cycle (21, 110) is reached, so the orbit of 0 is O(0) = {0, 1, 10, 11, 20, 101, 21, 110}, of size a(0) = 8. We may also deduce that a(1) = 7, a(10) = 6, a(11) = 5, a(20) = 4, a(101) = 3 and a(21) = a(110) = 2 which is the length of the cycle these elements belong to.
Similarly, 2 -> 100 -> 12 -> 110 -> 21 -> ..., so the orbit of 2 is O(2) = {2, 100, 12, 110, 21}, of size a(2) = 5. We also deduce a(100) = 4 and a(12) = 3.
Then, 3 -> 1000 -> 13 -> 1010 -> 22 -> 200 -> 102 -> 111 -> 30 -> 1001 -> 22 -> 200 -> ..., here the cycle (22, 200, 102, 111, 30, 1001) is reached, and we have the orbit O(3) = {3, 1000, 13, 1010, 22, 200, 102, 111, 30, 1001}, of size a(3) = 10, and also a(1000) = 9, a(13) = 8, a(1010) = 7 and a(n) = 6 for the elements of that cycle.
Crossrefs
Programs
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Mathematica
Array[-1 + Length@ NestWhileList[FromDigits@ RotateLeft@ Reverse@ DigitCount[#] &, #, UnsameQ[##] &, All] &, 60, 0] (* Michael De Vlieger, Nov 23 2021 *)
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PARI
apply( {A349250(n,S=[n])=while(!setsearch(S,n=A348783(n)),S=setunion(S,[n]));#S}, [0..99]) -
Python
def f(n): s = str(n) return int("".join(str(s.count(d)) for d in "9876543210").lstrip("0")) def a(n): orbit, fn = {n}, f(n) while fn not in orbit: orbit.add(fn) n, fn = fn, f(fn) return len(orbit) print([a(n) for n in range(70)]) # Michael S. Branicky, Nov 18 2021
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